Quantum Electromagnetic Radiation

Despite quantum theory’s remarkable success at predicting the statistical results of experiments, many philosophers worry that it nonetheless lacks some crucial connection between theory and experiment. Such worries constitute the Quantum Measurement Problems. One can broadly identify two kinds of worries: (1) pragmatic: it is unclear how to model our measurement processes in order to extract experimental predictions, and (2) realist: we lack a satisfying metaphysical account of measurement processes. While both issues deserve attention, the pragmatic worries have worse consequences if left unanswered: If our pragmatic theory-to-experiment linkage is unsatisfactory, then quantum theory is at risk of losing both its evidential support and its physical salience. Avoiding these risks is at the core of what I will call the Pragmatic Measurement Problem. Fortunately, the pragmatic measurement problem is not too difficult to solve. For non-relativistic quantum theory, the story goes roughly as follows: One can model each of quantum theory’s key experimental successes on a case-by-case basis by using a measurement chain. In modeling this measurement chain, it is pragmatically necessary to switch from using a quantum model to a classical model at some point. That is, it is pragmatically necessary to invoke a Heisenberg cut at some point along the measurement chain. Past this case-by-case measurement framework, one can then strive for a wide-scoping measurement theory capable of modeling all (or nearly all) possible measurement processes. For non-relativistic quantum theory, this leads us to our usual projective measurement theory. As a bonus, proceeding this way also gives us an empirically meaningful characterization of the theory’s observables as (positive) self-adjoint operators. But how does this story have to change when we move into the context of quantum field theory (QFT)? It is well known that in QFT almost all localized projective measurements violate causality, allowing for faster-than-light signaling; These are Sorkin’s impossible measurements. Thus, the story of measurement in QFT cannot end as it did before with a projective measurement theory. But does this then mean that we need to radically rethink the way we model measurement processes in QFT? Are our current experimental practices somehow misguided? Fortunately not. I will argue that (once properly understood) our old approach to modeling quantum measurements is still applicable in QFT contexts. We ought to first use measurement chains to build up a case-by-case measurement framework for QFT. Modeling these measurement chains will require us to invoke what I will call a QFT-cut. That is, at some point along the measurement chain we must switch from using a QFT model to a non-QFT model. Past this case-by-case measurement framework, we can then strive for both a new wide-scoping measurement theory for QFT and an empirically meaningful characterization of its observables. It is at this point that significantly more theoretical work is needed. This paper ends by briefly reviewing the state of the art in the physics literature regarding the modeling of measurement processes involving quantum fields.

Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

Strong convergence of the linear implicit Euler method for the finite element discretization of semilinear non-autonomous SPDEs driven by multiplicative or additive noise

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum system and its inseparable thermal bath, formally “entangled” like an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom (DDF) between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions.

An imaginary-time method was developed for calculating the probability of particle transmission through smooth barriers variable with time. Within the imaginary-time method, the tunneling process is described by using classical equations of motion written in terms of an imaginary time (t → it), while the probability of tunneling is determined by the imaginary part of the action functional, this imaginary part being calculated along the subbarrier particle trajectory. The fundamentals of the imaginary-time method are surveyed, and its applications in the theory of atomic-state ionization under the effect of constant electric and magnetic fields that have various configurations, in the field of intense monochromatic laser radiation and of an ultrashort electromagnetic pulse, in the process of Lorentz ionization of atoms and ions during their motion in a strong magnetic field, etc., are outlined. The applications of the imaginary-time method in relativistic cases—for example, in the theory of ionization of levels of multiply charged ions whose binding energy is commensurate with the electron rest energy—and in quantum field theory (Schwinger effect, which consists in the production of electron-positron pairs from a vacuum by a superstrong external field) are briefly described. Particular attention is given to methodological issues and details of the imaginary-time method that are of importance in solving specific physics problems, but which are usually skipped in original publications.

A cat state localized in the right Rindler wedge is employed to study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality in a relativistic scalar-free quantum field theory. By means of the bounded Hermitian operator <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>sign</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>φ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>f</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> , where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>φ</g:mi> <g:mo stretchy="false">(</g:mo> <g:mi>f</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms, which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.

The derivation of fundamental effects related to the rotation and acceleration of a medium consisting of relativistic particles based on quantum-statistical approaches is presented. The Unruh effect for an accelerated medium is derived based on the Zubarev density operator. A nonperturbative formula is obtained for the chiral vortical effect (CVE) in a medium with vorticity at a finite mass based on a generalization of the first terms of the quantum-field perturbation theory calculated using the statistical operator. Various corrections to these effects in higher orders in acceleration and vorticity were found. The concept of vorticity and acceleration as new real and imaginary chemical potentials is substantiated. The duality of the quantum-statistical Zubarev density operator and quantum field theory in a space-time with a conical singularity is revealed and shown by the example of the correspondence of quantum corrections with acceleration in two approaches. The consequences of this duality for both methods are investigated. A new effect related to thermodynamic instability at the Unruh temperature is shown.

Of the three organizers of the conference N. Hitchin is a mathematician, A. Kapustin and W. Nahm are physicists. Ideas from physics, in particular from string theory and related areas had a profound influence on algebraic and differential geometry. Conversely, many developments in string theory use very recent mathematical results. There were 19 talks at the workshop, 12 by mathematicians and 7 by physicists, but in many cases an outside observer would have had difficulties to sort them out. Quantum field theory often allows continuous interpolations between geometrical structures of topologically different manifolds. A particularly important example is mirror symmetry, where the complexified Kähler cone of one manifold corresponds to the moduli space of complex structures of the mirror manifold. Several talks explored geometrical and number theoretical aspects of this connection. Mirror symmetry can be understood in terms of torus fibrations and an isomorphism between the quantum field theories given by maps to a torus and to its dual (T-duality). The B-field of string theory can be described in terms of non-commutative geometry on the tori, and its effect on T-duality has been investigated. The quantum field theories which provide these dualities are supersymmetric conformally invariant quantum field theories in two dimensions. In mathematics, large parts of their structures have been axiomatised in the language of vertex operator algebras, but much remains to be done. A promising mathematical approach is provided by the chiral de Rham complex. This cohomology of this complex seems to be invariant under mirror symmetry, but its physical meaning is not yet clear. This led to many discussions between mathematicians and physicists. Indeed, the free time for discussions was at least as important as the lectures for learning the language of researchers with a different background and for making use of their ideas. An area in which the common understanding is well advance is topological field theory. Here one has good axioms and many of the analytic problems of conformally invariant quantum field theories can be ignored. One can solve rather complex problems and one can make contact with new geometrical ideas, in particular generalised complex structures. The latter allow to interpolate between complex and symplectic geometry, which should become important for both physics and mathematics. To understand all of conformal field theory at a similar mathematical depth will take more time, but already now relations to mixed Hodge structures have given much insight. Eventually many so far intractable problems should be solvable by the use of quantum field theoretical ideas, for example the construction of the non-singular Ricci flat metrics on K3. Perturbative string theory can be described in terms of conformal field theory, but the complete theory has more excitations than strings. Among them the best understood are the D-branes, many features of which can be understood in terms of boundary states in conformal field theory. Some of these branes are related to complex submanifolds, others to certain Lagrangian submanifolds, and their description involves twisted K-theory and derived categories. The development of a common language between mathematicians and physicists is well under way, and the workshop has made a contribution which all participants found very stimulating. In Europe such meetings between mathematicians and string theorists are rare, so the workshop was particularly useful. Much of the time was reserved for informal discussions. On one evening there was a discussion on the relation between classical and quantum geometry. Weather predictions for the free afternoon had been bad, but finally the weather was splendid and the supply of Black Forest cake matched the demand.

We briefly exhibit in this chapter the mathematical formalism of QFT, which actually has a non-trivial combinatorial backbone. The QFT setting can be understood as a quantum description of particles and their interactions, a description which is also compatible with Einstein's theory of special relativity. Within the framework of elementary particle physics (or high-energy physics), QFT led to the Standard Model of Elementary Particle Physics, which is the physical theory tested with the best accuracy by collider experiments. Moreover, the QFT formalism successfully applies to statistical physics, condensed matter physics and so on. We show in this chapter how Feynman graphs appear through the so-called QFT perturbative expansion, how Feynman integrals are associated to Feynman graphs and how these integrals can be expressed via the help of graph polynomials, the Kirchhoff–Symanzik polynomials. Finally, we give a glimpse of renormalization, of the Dyson–Schwinger equation and of the use of the so-called intermediate field method. This chapter mainly focuses on the so-called Phi? QFT scalar model.

One can consider the developments in quantum field theory from the point of view of foundational problems posed about physical reality at both the epistemological and ontological levels, or as a ‘laboratory’ to study the actual methodology of the scientific enterprise. I shall address both of these issues in this paper. My contention is that at the foundational level there is essentially nothing new in quantum field theory that is not already present in non-relativistic quantum mechanics. This is quite different in emphasis from the view expressed by Redhead (1983a). Even in quantum mechanics most of the difficulties which arise are generated by the realist’s inclination to take the formalism too literally as representing physical reality, often in a modified or distorted classical view. More serious consideration of Bohr’s philosophical framework of complementarity may prove fruitful for coping with this problem, which is not new to quantum field theory, being already the central interpretative problem of quantum mechanics. On the other hand, as a source to illustrate how theories arc constructed and established in actual scientific practice, quantum field theory does provide a wide range of useful examples. Here too, although there are many technically fascinating topics (such as renormalization), quantum field theory is pretty much (meth odological) business as usual. Much more interesting, essentially new, methodological departures are seriously proposed (with varying degrees of credibility) by some rival or alternative developments in modern theoretical physics, such as the S-matrix programme, with its bootstrap conjecture, or cosmology, with various forms of the anthropic principle (Gale 1983) and with the inflationary universe scenario (Guth 1981 ).

Rom Harre & Harvey Brown both of the University of Oxford: Introduction I. QUANTUM FIELD THEORY AS AN OBJECT OF PHILOSOPHICAL STUDY: TWO VIEWS: Michael Redhead, University of Cambridge: A philosopher looks at quantum field theory James T. Cushing, University of Notre Dame: Foundational problems in and methodological lessons from quantum field theory II. THE PROBLEMS OF VIRTUAL PARTICLES AND RENORMALIZATION: Robert Weingard, Rutgers University: Virtual particles and the interpretation of quantum field theory Rom Harre: Parsing the amplitudes Paul Teller, University of Illinois: Three problems of renormalization III. COVARIANCE PRINCIPLES IN QUANTUM FIELD THEORY: Gordon N. Fleming, Pennsylvania State University: Hyperplane-dependent quantized fields and Lorentz invariance Tian-yu Cao, Trinity College, Cambridge: Gauge theory and the geometrization of fundamental physics IV. MATHEMATICAL FOUNDATIONS OF QUANTUM FIELD THEORY: Ray F. Streater, King's College, London: Why should anyone want to axiomatize quantum field theory? Simon Saunders, Wolfson College, Oxford: The algebraic notation of quantum field theory.

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researchers in theoretical physics, especially those with an interest in experimental and theoretical particle physics and quantum field theory.

Finite element approximation in quantum field theory

The holographic principle implies that quantum field theory (QFT) overcounts the number of independent degrees of freedom in quantum gravity. An argument due to Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom well described by QFT is even smaller than required by holographic bounds, and CKN interpreted this result as indicative of a correlation between the UV and IR cutoffs on QFT. Here, we consider an alternative interpretation in which the QFT degrees of freedom are depleted as a function of scale. We use a simple recipe to estimate the impact of depleted densities of states on precision observables, including the Lamb shift and lepton $g\ensuremath{-}2$. Although these observables are not sensitive to the level of depletion motivated by gravitational considerations, the phenomenological exercises also provide an interesting test of quantum field theory that is independent of underlying quantum gravity assumptions. A depleted density of states can also render the QFT vacuum energy UV insensitive, reconciling the success of QFT in describing ordinary particle physics processes and its apparent failure in predicting the cosmological constant.

Fortran code for SU(3) lattice gauge theory with and without MPI checkerboard parallelization