Foundations Of Quantum Field Theory Research Articles

Perturbative expansions and the foundations of quantum field theory

Perturbative expansions and the foundations of quantum field theory

What if ϕ4 theory in 4 dimensions is non-trivial in the continuum?

Traditionally, scalar ϕ4 theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that they do not actually cover all physically meaningful situations, in particular the case of multi-component fields and non-polynomial action. In this work, I study multi-component scalar field theories in four dimensions in the continuum and show that they do evade the apparently foregone conclusion of triviality. Instead, one finds a non-trivial interacting theory that has two phases, bound states and non-trivial scattering amplitudes in the limit of many components. This has potentially broad implications, both for the foundations of quantum field theory as well as for the experimentally accessible Higgs sector of the Standard Model.

Axion–neutrino couplings, late-time phase transitions and the far infrared physics

The far infrared physics is a fascinating topic for theoretical physics, since the foundation of quantum field theory and neutrinos seem to be strongly related with the far infrared physics of our Universe. In this work we shall explore the possibility of a late-time thermal phase transition caused by the axion–neutrino interactions. The axion is assumed to be the misalignment axion which is coupled primordially to a chiral symmetric neutrino. The chiral symmetry is supposed to be broken either spontaneously or explicitly, and two distinct phenomenological models of axion–neutrinos are constructed. The axion behaves as cold dark matter during all its evolution eras, however if we assume that the axion and the neutrino fields interact coherently in a classical way as fields, or as ensembles, then we consider thermal effects in the axion sector, due to the values of operators ϕ for the axion and ν̄ν due to the neutrinos. The thermal equilibrium between the two has no effect to the axion effective potential for a wide temperature range. As we show, contrary to the existing literature, the axion never becomes destabilized due to the finite temperature effects, however if axion-Higgs higher order non-renormalizable operators are present in the Lagrangian, the axion potential is destabilized in the temperature range T∼0.1MeV down to T∼0.01eV and a first order phase transition takes place. The initial axion vacuum decays to the energetically more favorable axion vacuum, and the latter decays to the Higgs vacuum which is more preferable. This late-time phase transition might take place in the redshift range z∼385−37 and thus it may cause density fluctuations in the post-recombination era. This might be the source of large scale matter structure at high redshifts z≥9. Following the literature, we qualitatively discuss the implications of such a late-time phase transition at the astrophysical and cosmological level.

Conserved relativistic Ertel’s current generating the vortical and thermodynamic aspects of space–time

Motivated by Aoki et al.’s recent research on conserved charges and entropy current, we reinvestigated the conservation of relativistic Ertel’s current, which has received little attention outside the field of geophysical fluid dynamics. Ertel’s charge is an important indicator of the correlation between vortex vectors and entropy gradient fields in Earth’s meridional heat transport. We first show that in the generalized Hamiltonian structure of baroclinic fluids, the duality between the total energy and the Casimir as a function of Ertel’s charge plays an important role in the nonrelativistic case. Then, by extending the result to relativistic cases, we show that this finding has far-reaching implications not only for space–time issues in cosmology but also for the foundation of quantum field theory. An especially important finding is that, as an unreported dual form of the Einstein field equation, we identify a special equation satisfied not only by the vortex tensor field generated by the conserved charge but also by the Weyl tensor in interpreting the physical nature of the metric tensor [Formula: see text], which appears in the cosmological term [Formula: see text].

The Divergence of Van Hove’s Model and its Consequences

We study a regularized version of Van Hove’s 1952 model, in which a quantum field interacts linearly with sources of finite width lying at fixed positions. We show that the central result of Van Hove’s 1952 paper on the foundations of Quantum Field Theory, the orthogonality between the spaces of state vectors which correspond to different values of the parameters of the theory, disappears when a well-defined model is considered. We comment on the implications of our results for the contemporary relevance of Van Hove’s article.

A concise introduction to quantum field theory

We review the basic principles of Quantum Field Theory (QFT) in a brief but comprehensive introduction to the foundations of QFT. The principles of QFT are introduced in canonical and covariant formalisms. The problem of ultraviolet (UV) divergences and its renormalization is analyzed in the canonical formalism. As an application, we review the roots of Casimir effect. For simplicity, we focus on the scalar field theory but the generalization for fermion fields is straightforward. However, the quantization of gauge fields require extra techniques which are beyond the scope of this paper. The special cases of free field theories and conformal invariant theories in lower space-time dimensions illustrate the relevance of the foundations of the theory. Finally, a short introduction to functional integrals and perturbation theory in the Euclidean formalism is included in the last section.

No-Go Theorems and the Foundations of Quantum Physics

In the history of quantum physics several no-go theorems have been proved, and many of them have played a central role in the development of the theory, such as Bell’s or the Kochen–Specker theorem. A recent paper by F. Laudisa has raised reasonable doubts concerning the strategy followed in proving some of these results, since they rely on the standard framework of quantum mechanics, a theory that presents several ontological problems. The aim of this paper is twofold: on the one hand, I intend to reinforce Laudisa’s methodological point by critically discussing Malament’s theorem in the context of the philosophical foundation of quantum field theory; secondly, I rehabilitate Gisin’s theorem showing that Laudisa’s concerns do not apply to it.

Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe.

The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.

A philosopher's guide to the foundations of quantum field theory

AbstractA major obstacle facing interpreters of quantum field theory (QFT) is a proliferation of different theoretical frameworks. This article surveys three of the main available options—Lagrangian, Wightman, and algebraic QFT—and examines how they are related. Although each framework emphasizes different aspects of QFT, leading to distinct strengths and weaknesses, there is less tension between them than commonly assumed. Given the limitations of our current knowledge and the need for creative new ideas, I urge philosophers to explore puzzles, tools, and techniques from all three approaches.

Quantum Walks, Weyl Equation and the Lorentz Group

Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata and walks starting from very general principles. The intrinsic discreteness of this framework is reconciled with the continuous Lorentz symmetry by reformulating the notion of inertial reference frame in terms of the constants of motion of the quantum walk dynamics. In particular, among the symmetries of the quantum walk which recovers the Weyl equation--the so called Weyl walk--one finds a non linear realisation of the Poincar\'e group, which recovers the usual linear representation in the small wave-vector limit. In this paper we characterise the full symmetry group of the Weyl walk which is shown to be a non linear realization of a group which is the semidirect product of the Poincar\'e group and the group of dilations.

The Geometry of Noncommutative Spacetimes

We review the concept of ‘noncommutative spacetime’ approached from an operational stand-point and explain how to endow it with suitable geometrical structures. The latter involves i.a. the causal structure, which we illustrate with a simple—‘almost-commutative’—example. Furthermore, we trace the footprints of noncommutive geometry in the foundations of quantum field theory.

Gravitation, Quantum Mechanics and the Least Action Electromagnetic Equilibrium States

The century old challenge of fundamental physics has been to reconcile quantum mechanics (QM) that deals with submicroscopic interactions between elementary particles from the quantization perspective, with relativistic mechanics that deals with gravitation at the macroscopic level from the infinitesimally progressive perspective, mainly embodied by the theory of general relativity (GR). The ease with which infinitesimally progressive sequences of motion can be mathematically represented by means of an indefinite number of instantaneous momentary excited states of a postulated underlying neutral energy quantum vacuum field, which is the foundation of quantum field theory (QFT), has naturally privileged this quantization perspective in all past attempts at reconciling QM with gravitation. But, given that all scatterable elementary particles identifiable within atomic structures have an electrical charge, and are thus electromagnetic in nature, this article explores the possibility of reconciling quantum mechanics with relativistic mechanics from the electromagnetic perspective, by means of reconciling the wave function with the least action electromagnetic resonance states into which elementary charged particles become captive within atomic and nuclear structures, and ultimately, with gravitation.

Analogue cosmology in a hadronic fluid

Analog gravity models of general relativity seem promising routes to providing laboratory tests of the foundation of quantum field theory in curved space-time. In contrast to general relativity, where geometry of a spacetime is determined by the Einstein equations, in analog models geometry and evolution of analog spacetime are determined by the equations of fluid mechanics. In this paper we study the analogue gravity model based on massless pions propagating in a expanding hadronic fluid. The analog expanding spacetime takes the form of an FRW universe, with the apparent and trapping horizons defined in the standard way.

Testing Lorentz invariance in the weak decay of polarized atoms

Symmetries of space time, and Lorentz and CPT symmetry in particular, are a cornerstone of modern physics and lie at the foundation of quantum field theory (QFT) and Einstein's theory of general relativity, the two most successful theories in physics which together describe the four fundamental forces of nature. However, the inability to incorporate gravity as described by general relativity into the QFT standard model of particle physics, which very successfully combines the electromagnetic, strong and weak interactions, has led to the development of alternative so-called Grand Unified Theories (GUTs) or theories of quantum gravity. Since many of these theories break Lorentz symmetry at some small level 1-4, experimental searches for Lorentz-violating effects could help shed light on new physics beyond the standard model (SM) and provide clues as to the nature of quantum gravity. Parameterization of such effects within the Lorentz-violating Standard Model Extension (SME) developed by A. Kostelecky 5 has allowed direct comparison of many experiments, ranging from table-top precision measurements to observations of ultra-high energy cosmic and gamma rays to astrophysical observations. The SME has proven to be a remarkable tool in the search for Lorentz violation across the landscape of experimental physics. Up until the present, experimental results have taken the form of upper bounds on the SME coefficients and are tabulated in the Data Tables for Lorentz and CPT Violation 6. On a closer look, however, Lorentz invariance has been tested poorly in the weak interaction 7, 8, which is all the more surprising since violations of fundamental symmetries could be observed only in the weak sector: The first discovery of a violation of presumed (discrete) space-time symmetry was that of parity violation in nuclear β decay 9. C. S. Wu and her collaborators found that when a specific nucleus (60Co) was placed in a magnetic field, electrons from the beta decay were preferentially emitted in the direction opposite that of the aligned angular momentum of the nucleus. When it is possible to distinguish these two cases in a mirror, parity is not conserved. If the mirror not only reverses spatial direction but also changes matter to antimatter, then the experiment in front of the mirror would look just like its mirror image. The separate violations of P symmetry and C symmetry cancel to preserve CP symmetry. These symmetry violations arise only from the weak interaction, not from the strong and electromagnetic interactions, and therefore shows up strongly only in beta decay. Until 1964 it was thought that the combination CP was a valid symmetry of the Universe. That year, Christenson, Cronin, Fitch, and Turlay performed their historic experiment to see if the long-lived neutral K meson could occasionally decay to π+ π−. They found that indeed it did 10! And the observed CP violation implies, by CPT invariance, violations of T-symmetry as well.

What is what we call the ‘quantum field’? Answering from a teaching perspective by taking the foundations into account

Within physics education research a number of teaching proposals aimed at introducing elements of particle physics into secondary-school and introductory-university-level courses have been produced in recent years. Many of them face the problem of introducing the notion of the quantum field, which has a central role in contemporary physics. In this paper two representative examples are discussed; it is shown that both of them take the standard approach to introducing quantum field theory at university level (the ‘canonical quantization approach’) as their reference and that at the same time they introduce some ideas regarding quantum fields that are problematic when recent studies of the foundations of quantum field theory are taken into account. Starting from recent reformulations of quantum field theory, a different perspective to the notion of the quantum field is presented and a certain number of original insights that seem to be promising from a teaching perspective are emphasized.

Experimental tests of Quantum Mechanics: from Pauli Exclusion Principle Violation to spontaneous collapse models

The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, is at the very basis of our understanding of matter. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the q violation parameter translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the q-parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (Violation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter and as probability of PEP violation, we briefly discuss the results and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopic fast Silicon Drift Detectors. We mention as well the possibility of using a similar experimental technique to search for eventual X-rays generated as a signature of the spontaneous collapse of the wave function, predicted by continuous spontaneous localization type theories.

Experimental tests of quantum mechanics – Pauli exclusion principle violation (the VIP experiment) and future perspective

The Pauli exclusion principle (PEP), consequence of the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, as many other fundamental principles it spurs a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. The VIP (VIolation of the Pauli exclusion principle) experiment established a new limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental setup. We also shortly mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models in quantum mechanics.

Experimental tests of quantum mechanics: Pauli Exclusion Principle Violation (the VIP experiment) and future perspectives

The Pauli exclusion principle (PEP), as a consequence or the spin-statistics connection, is one of the basic principles of the modern physics. Being at the very basis of our understanding of matter, it spurs a lively debate on its possible limits, deeply rooted as it is in the very foundations of Quantum Field Theory. The VIP (VIolation of the Pauli exclusion principle) experiment established the world's best limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method and the obtained results; we briefly present future plans to go beyond the actual limit by upgrading the experiment using vetoed new spectroscopic fast Silicon Drift Detectors. We also shortly mention the possibility of using a similar experimental technique to search for possible X-rays generated in the spontaneous collapse models of quantum mechanics.

EXPERIMENTAL TESTS OF QUANTUM MECHANICS PAULI EXCLUSION PRINCIPLE VIOLATION (THE VIP EXPERIMENT) AND FUTURE PERSPECTIVES

The Pauli exclusion principle (PEP) is one of the basic principles of modern physics. Being at the very basis of our understanding of matter, as many other fundamental principles it spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Field Theory. Therefore, it is extremely important to test the limits of its validity. Quon theory provides a suitable mathematical framework of possible violation of PEP, where the violation parameter q translates into a probability of violating PEP. Experimentally, setting a bound on PEP violation means confining the violation parameter to a value very close to either 1 (for bosons) or -1 (for fermions). The VIP (VIolation of the Pauli exclusion principle) experiment established a limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, both in terms of the q-parameter from quon theory and as probability of PEP violation, we briefly discuss them and present future plans to go beyond the actual limit by upgrading the experimental technique using vetoed new spectroscopical fast Silicon Drift Detectors. We also shortly mention the possibility of using a similar experimental technique to search for eventual X-rays, generated in the spontaneous collapse models.

ELECTROMAGNETIC KLEIN–GORDON AND DIRAC EQUATIONS IN SCALE RELATIVITY

We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schrödinger, Klein–Gordon, Dirac, Pauli) have been derived as geodesic equations written with a quantum-covariant derivative operator. Then, the nature of gauge transformations, of gauge fields and of conserved charges have been given a geometric meaning in terms of a scale-covariant derivative tool. Finally, the electromagnetic Klein–Gordon equation has been recovered with a covariant derivative constructed by combining the quantum-covariant velocity operator and the scale-covariant derivative. We show here that if one tries to derive the electromagnetic Dirac equation from the Klein–Gordon one as for the free particle motion, i.e. as a square root of the time part of the Klein–Gordon operator, one obtains an additional term which is the relativistic analog of the spin-magnetic field coupling term of the Pauli equation. However, if one first applies the quantum covariance, then implements the scale covariance through the scale-covariant derivative, one obtains the electromagnetic Dirac equation in its usual form. This method can also be applied successfully to the derivation of the electromagnetic Klein–Gordon equation. This suggests it rests on more profound roots of the theory, since it encompasses naturally the spin–charge coupling.