S Tani, Note on the Formal Solution of the Tomonaga-Schwinger Equation, Prog. Theor. Phys., .
We shall present here some remarks on the formal solution of the Tomonaga - Schwinger . equation of field theory. However, the physical interpretation of these formal solutions will be left for future works which will come into contact with the fundamental difficulties underlying our present …
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Ken A Dill and Justin L MacCallum, The Protein-Folding Problem, 50 Years On, Science, 338 (2012) 1042-1046.
The protein-folding problem was first posed about one half-century ago. The term refers to three broad questions: (i) What is the physical code by which an amino acid sequence dictates a protein’s native structure? (ii) How can proteins fold so fast? (iii) Can we devise a computer algorithm to predict protein structures from their sequences? We review progress on these problems. In a few cases, computer simulations of the physical forces in chemically detailed models have now achieved the accurate folding of small proteins. We have learned that proteins fold rapidly because random thermal motions cause conformational changes leading energetically downhill toward the native structure, a principle that is captured in funnel-shaped energy landscapes. And thanks in part to the large Protein Data Bank of known structures, predicting protein structures is now far more successful than was thought possible in the early days. What began as three questions of basic science one half-century ago has now grown into the full-fledged research field of protein physical science.
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Julian Schwinger, Quantum Electrodynamics. I. A Covariant Formulation, Physical Review, 74 (1948) 1439-1461.
Attempts to avoid the divergence difficulties of quantum electrodynamics by multilation of the theory have been uniformly unsuccessful. The lack of convergence does indicate that a revision of electrodynamic concepts at ultrarelativistic energies is indeed necessary, but no appreciable alteration of the theory for moderate relativistic energies can be tolerated. The elementary phenomena in which divergences occur, in consequence of virtual transitions involving particles with unlimited energy, are the polarization of the vacuum and the self-energy of the electron, effects which essentially express the interaction of the electromagnetic and matter fields with their own vacuum fluctuations. The basic result of these fluctuation interactions is to alter the constants characterizing the properties of the individual fields, and their mutual coupling, albeit by infinite factors. The question is naturally posed whether all divergences can be isolated in such unobservable renormalization factors; more specifically, we inquire whether quantum electrodynamics can account unambiguously for the recently observed deviations from the Dirac electron theory, without the introduction of fundamentally new concepts. This paper, the first in a series devoted to the above question, is occupied with the formulation of a completely covariant electrodynamics. Manifest covariance with respect to Lorentz and gauge transformations is essential in a divergent theory since the use of a particular reference system or gauge in the course of calculation can result in a loss of covariance in view of the ambiguities that may be the concomitant of infinities. It is remarked, in the first section, that the customary canonical commutation relations, which fail to exhibit the desired covariance since they refer to field variables at equal times and different points of space, can be put in covariant form by replacing the four-dimensional surface $t=\mathrm{const}$. by a space-like surface. The latter is such that light signals cannot be propagated between any two points on the surface. In this manner, a formulation of quantum electrodynamics is constructed in the Heisenberg representation, which is obviously covariant in all its aspects. It is not entirely suitable, however, as a practical means of treating electrodynamic questions, since commutators of field quantities at points separated by a time-like interval can be constructed only by solving the equations of motion. This situation is to be contrasted with that of the Schr\"odinger representation, in which all operators refer to the same time, thus providing a distinct separation between kinematical and dynamical aspects. A formulation that retains the evident covariance of the Heisenberg representation, and yet offers something akin to the advantage of the Schr\"odinger representation can be based on the distinction between the properties of non-interacting fields, and the effects of coupling between fields. In the second section, we construct a canonical transformation that changes the field equations in the Heisenberg representation into those of non-interacting fields, and therefore describes the coupling between fields in terms of a varying state vector. It is then a simple matter to evaluate commutators of field quantities at arbitrary space-time points. One thus obtains an obviously convariant and practical form of quantum electrodynamics, expressed in a mixed Heisenberg-Schr\"odinger representation, which is called the interaction representation. The third section is devoted to a discussion of the covariant elimination of the longitudinal field, in which the customary distinction between longitudinal and transverse fields is replaced by a suitable covariant definition. The fourth section is concerned with the description of collision processes in terms of an invariant collision operator, which is the unitary operator that determines the over-all change in state of a system as the result of interaction. It is shown that the collision operator is simply related to the Hermitian reaction operator, for which a variational principle is constructed.
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Liang Shan, Consciousness Is an Entity with Entangled States: Correlating the Measurement Problem with Non-Local Consciousness , , 2018 pp. 1-126.
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Fang Huang et al., Distinguishing between cooperative and unimodal downhill protein folding, Proceedings Of The National Academy Of Sciences Of The United States Of America, 104 (2007) 123-127.
Conventional cooperative protein folding invokes discrete ensembles of native and denatured state structures in separate free-energy wells. Unimodal noncooperative (“downhill”) folding, however, proposes an ensemble of states occupying a single free-energy well for proteins folding at ≥4 × 104 s−1 at 298 K. It is difficult to falsify unimodal mechanisms for such fast folding proteins by standard equilibrium experiments because both cooperative and unimodal mechanisms can present the same time-averaged structural, spectroscopic, and thermodynamic properties when the time scale used for observation is longer than for equilibration. However, kinetics can provide the necessary evidence. Chevron plots with strongly sloping linear refolding arms are very difficult to explain by downhill folding and are a signature for cooperative folding via a transition state ensemble. The folding kinetics of the peripheral subunit binding domain POB and its mutants fit to strongly sloping chevrons at observed rate constants of >6 × 104 s−1 in denaturant solution, extrapolating to 2 × 105 s−1 in water. Protein A, which folds at 105 s−1 at 298 K, also has a well-defined chevron. Single-molecule fluorescence energy transfer experiments on labeled Protein A in the presence of denaturant demonstrated directly bimodal distributions of native and denatured states.
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S Hashimoto, 18. Lattice Quantum Chromodynamics, , 2014 pp. 1-26.
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Anon. (2020), Reflections upon the Emergence of Hadronic Mass , , 2020 pp. 1-13.
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John D Barrow, Inconstant Contsants, , 2005 pp. 1-3.
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Zohreh Davoudi, The path from finite to infinite volume: Hadronic observables from lattice QCD, Arxiv.Org, 2018 1812.11899v1, hep-lat.
Standard Model determinations of properties of strongly interacting systems of hadrons have become possible with the powerful method of lattice quantum chromodynamics (LQCD), a method with growing applicability and reliability. While growth in computational power and innovations in algorithmic and computational approaches have been essential in advancing the state of the field, conceptual and formal developments have played a crucial role in turning the output of LQCD computations to phenomenologically valuable results. From the invention of finite-volume technology to access physical observables by Martin L\"uscher over three decades ago to date, this field has grown in scope and complexity, enabling studies of scattering amplitudes and reaction rates, as well as spectroscopy of excited states of quantum chromodynamics (QCD) and resonances. Further, LQCD studies are augmented with the inclusion of quantum electrodynamics (QED), and subtleties related to the finite volume of systems in presence of QED have been understood and largely controlled. In this talk, I focus on selected developments to give a taste of the status of the field concerning the mapping between the finite and infinite-volume physics and its state-of-the-art applications.
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D Djukanovic et al., Derivation of spontaneously broken gauge symmetry from the consistency of effective field theory II: Scalar field self-interactions and the electromagnetic interaction, Arxiv.Org, hep-th (2018) 436-441.
We extend our study of deriving the local gauge invariance with spontaneous symmetry breaking in the context of an effective field theory by considering self-interactions of the scalar field and inclusion of the electromagnetic interaction. By analyzing renormalizability and the scale separation conditions of three-, four- and five-point vertex functions of the scalar field, we fix the two couplings of the scalar field self-interactions of the leading order Lagrangian. Next we add the electromagnetic interaction and derive conditions relating the magnetic moment of the charged vector boson to its charge and the masses of the charged and neutral massive vector bosons to each other and the two independent couplings of the theory. We obtain the bosonic part of the Lagrangian of the electroweak Standard Model as a unique solution to the conditions imposed by the self-consistency conditions of the considered effective field theory.
Published in: Phys. Lett. B 788 (2019) 436-441
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Freeman J Dyson, Tomonaga, Schwinger, and Feynman Awarded Nobel Prize for Physics, Science, 150 (1965) 588-589.
The 1965 Nobel prize for physics has been awarded to three theorists, Sin-Itiro Tomonaga of Tokyo, Julian Schwinger of Harvard, and Richard Feynman of the California Institute of Technology. The prize was given for their creation of the modern theory of quantum …
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J D Fraser, Towards a Realist View of Quantum Field Theory, , 2018.
Quantum field theories (QFTs) seem to have all of the qualities that typically motivative scientific realism. Alongside general relativity, the standard model of particle physics, and its subsidiaries, like quantum electrodynamics (QED) and quantum chromodynamics (QCD), are our most fundamental physical theories. They have also produced some of the most accurate predictions in the history of science: QED famously gives a value for the anomalous magnetic moment of the electron that agrees with experiment at precisions better than one …
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Ricardo Heras, Dirac quantisation condition: a comprehensive review, Arxiv.Org, physics.hist-ph (2018) 331-355.
In most introductory courses on electrodynamics, one is taught the electric charge is quantised but no theoretical explanation related to this law of nature is offered. Such an explanation is postponed to graduate courses on electrodynamics, quantum mechanics and quantum field theory, where the famous Dirac quantisation condition is introduced, which states that a single magnetic monopole in the Universe would explain the electric charge quantisation. Even when this condition assumes the existence of a not-yet-detected magnetic monopole, it provides the most accepted explanation for the observed quantisation of the electric charge. However, the usual derivation of the Dirac quantisation condition involves the subtle concept of an "unobservable" semi-infinite magnetised line, the so-called "Dirac string," which may be difficult to grasp in a first view of the subject. The purpose of this review is to survey the concepts underlying the Dirac quantisation condition, in a way that may be accessible to advanced undergraduate and graduate students. Some of the discussed concepts are gauge invariance, singular potentials, single-valuedness of the wave function, undetectability of the Dirac string and quantisation of the electromagnetic angular momentum. Five quantum-mechanical and three semi-classical derivations of the Dirac quantisation condition are reviewed. In addition, a simple derivation of this condition involving heuristic and formal arguments is presented.
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W Hollik, Electroweak Theory, Arxiv.Org, 1996 hep-ph/9602380v1, hep-ph.
In these lectures we give a discussion of the structure of the electroweak standard model and its quantum corrections for tests of the electroweak theory. The predictions for the vector boson masses, neutrino scattering cross sections and the Ζ resonance observables are presented in some detail. We show comparisons with the recent experimental data and their implications for the present status of the Standard Model. Finally we address the question how virtual New Physics can influence the predictions for the precision observables and discuss the minimal supersymmetric standard model as a special example of particular theoretical interest.
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Gregg Jaeger, Are Virtual Particles Less Real?, Entropy, 21 (2019) 141-17.
The question of whether virtual quantum particles exist is considered here in light of previous critical analysis and under the assumption that there are particles in the world as described by quantum field theory. The relationship of the classification of particles to quantum-field-theoretic calculations and the diagrammatic aids that are often used in them is clarified. It is pointed out that the distinction between virtual particles and others and, therefore, judgments regarding their reality have been made on basis of these methods rather than on their physical characteristics. As such, it has obscured the question of their existence. It is here argued that the most influential arguments against the existence of virtual particles but not other particles fail because they either are arguments against the existence of particles in general rather than virtual particles per se, or are dependent on the imposition of classical intuitions on quantum systems, or are simply beside the point. Several reasons are then provided for considering virtual particles real, such as their descriptive, explanatory, and predictive value, and a clearer characterization of virtuality—one in terms of intermediate states—that also applies beyond perturbation theory is provided. It is also pointed out that in the role of force mediators, they serve to preclude action-at-a-distance between interacting particles. For these reasons, it is concluded that virtual particles are as real as other quantum particles.
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Hagen Kleinert and Verena Schulte-Frohlinde, Critical Properties of φ4-Theories, , 2012 pp. 1-539.
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Elisabeth Kraus and Stefan Groot Nibbelink, Renormalization of the Electroweak Standard Model, Arxiv.Org, 1998 hep-th/9809069v1, hep-th.
These lecture notes give an introduction to the algebraic renormalization of the Standard Model. We start with the construction of the tree approximation and give the classical action and its defining symmetries in functional form. These are the Slavnov-Taylor identity, Ward identities of rigid symmetry and the abelian local Ward identity. The abelian Ward identity ensures coupling of the electromagnetic current in higher orders of perturbation theory, and is the functional form of the Gell-Mann-Nishijima relation. In the second part of the lectures we present in simple examples the basic properties of renormalized perturbation theory: scheme dependence of counterterms and the quantum action principle. Together with an algebraic characterization of the defining symmetry transformations they are the ingredients for a scheme independent unique construction of Green's functions to all orders of perturbation theory.
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Emanuele Mereghetti, Lattice QCD and nuclear physics for searches of physics beyond the Standard Model, Arxiv.Org, 2018 1812.11238v1, hep-lat.
Low-energy tests of fundamental symmetries are extremely sensitive probes of physics beyond the Standard Model, reaching scales that are comparable, if not higher, than directly accessible at the energy frontier. The interpretation of low-energy precision experiments and their connection with models of physics beyond the Standard Model relies on controlling the theoretical uncertainties induced by the nonperturbative nature of QCD at low energy and of the nuclear interactions. In these proceedings, I will discuss how the interplay of Lattice QCD and nuclear Effective Field Theories can lead to improved predictions for low-energy experiments, with controlled uncertainties. I will describe the framework of chiral Effective Field Theory, and then discuss a few examples, including non-standard β decays, neutrinoless double beta decay and searches for electric dipole moments, to highlight the progress achieved in recent years, and the role that Lattice QCD will play in addressing the remaining open problems.
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S Rivat, Renormalization scrutinized, Studies In History And Philosophy Of Science Part B, 2019.
In this paper, I propose a general framework for understanding renormalization by drawing on the distinction between effective and continuum Quantum Field Theories (QFTs), and offer a comprehensive account of perturbative renormalization on this basis. My central …
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S Tomonaga, On a relativistically invariant formulation of the quantum theory of wave fields, Prog. Theor. Phys., 1 (1946) 27-42.
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C G Torre and M Varadarajan, Functional Evolution of Free Quantum Fields, Arxiv.Org, hep-th (1998) 2651-2668.
We consider the problem of evolving a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show that this canonical transformation cannot, in general, be unitarily implemented on the Fock space for free quantum fields on flat spacetimes of dimension greater than 2. We do this by considering time evolution of a free Klein-Gordon field on a flat spacetime (with toroidal Cauchy surfaces) starting from a flat initial surface and ending on a generic final surface. The associated Bogolubov transformation is computed; it does not correspond to a unitary transformation on the Fock space. This means that functional evolution of the quantum state as originally envisioned by Tomonaga, Schwinger, and Dirac is not a viable concept. Nevertheless, we demonstrate that functional evolution of the quantum state can be satisfactorily described using the formalism of algebraic quantum field theory. We discuss possible implications of our results for canonical quantum gravity.
Published in: Class.Quant.Grav. 16 (1999) 2651-2668
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David Wallace, In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory, Synthese, 151 (2006) 33-80.
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Leanne K Wilkins, What QCD Tells Us About Nature -- and Why We Should Listen, Arxiv.Org, hep-ph (1999) 3c-20c.
I discuss why QCD is our most perfect physical theory. Then I visit a few of its current frontiers. Finally I draw some appropriate conclusions.
Published in: Nucl.Phys. A663 (2000) 3-20
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Leanne K Wilkins, Fundamental Constants, Arxiv.Org, 2007 0708.4361v1, hep-ph.
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric meaning. The ordinary gravitational constant parameterizes the stiffness, or resistance to curvature, of space-time. The cosmological term parameterizes space-time's resistance to expansion -- which may be, and apparently is at present, a { negative} resistance, i.e. a tendency toward expansion. The three gauge couplings of the strong, electromagnetic, and weak interactions parameterize resistance to curvature in internal spaces. The remaining fundamental couplings, of which there are a few dozen, supply an ungainly accommodation of inertia. The multiplicity and variety of fundamental constants are esthetic and conceptual shortcomings in our present understanding of foundational physics. I discuss some ideas for improving the situation. I then briefly discuss additional constants, primarily cosmological, that enter into our best established present-day world model. Those constants presently appear as macroscopic state parameters, i.e. as empirical ``material constants'' of the Universe. I mention a few ideas for how they might become fundamental constants in a future theory. In the course of this essay I've advertised several of my favorite speculations, including a few that might be tested soon.
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