scholarly journals From Gauge Anomalies to Gerbes and Gerbal Representations: Group Cocycles in Quantum Theory

10.14311/1189 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
J. Mickelsson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Representation Theory ◽  
Group Cohomology ◽  
Quantum Field ◽  
Yang Mills ◽  
Gauge Anomalies

In this paper I shall discuss the role of group cohomology in quantum mechanics and quantum field theory. First, I recall how cocycles of degree 1 and 2 appear naturally in the context of gauge anomalies. Then we investigate how group cohomology of degree 3 comes from a prolongation problem for group extensions and we discuss its role in quantum field theory. Finally, we discuss a generalization to representation theory where a representation is replaced by a 1-cocycle or its prolongation by a circle, and point out how this type of situations come up in the quantization of Yang-Mills theory.

Theories in History and Practice

2020 ◽  
pp. 203-224
Author(s):  
Steven French
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Field ◽  
Interpretive Practices ◽  
Classical And Quantum Mechanics

This eliminativist view must immediately face the concern that scientists themselves appear to be committed to the existence of theories. They talk about them, apparently refer to them, argue that they are equivalent or not and so forth. However, here it is shown that when it comes to classical and quantum mechanics, as well as quantum field theory—to give just three examples—what is meant by the theory is hugely contested. Indeed, this meaning is typically constructed retrospectively and promulgated by various means, such as through the use of certain textbooks, for example. Likewise it is contentious whether two putative formulations of the ‘same’ theory should be regarded as equivalent or not and again the role of interpretive practices comes to the fore.

scholarly journals Classical instanton solutions in quantum field theory

2020 ◽  
pp. 78-85
Author(s):  
Roman G. Shulyakovsky ◽  
Alexander S. Gribowsky ◽  
Alexander S. Garkun ◽  
Maxim N. Nevmerzhitsky ◽  
Alexei O. Shaplov ◽  
...  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Yukawa Potential ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Quantum Field ◽  
Two Dimensional ◽  
Yang Mills ◽  
The One

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

Scientific Realism and the Quantum

2020 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Scientific Realism ◽  
Quantum Physics ◽  
Quantum Field ◽  
Third Way ◽  
The World ◽  
Modern Physics

Scientific realism has traditionally maintained that our best scientific theories can be regarded as more or less true and as representing the world as it is (more or less). However, one of our very best current theories—quantum mechanics—has famously resisted such a realist construal, threatening to undermine the realist stance altogether. The chapters in this volume carefully examine this tension and the reasons behind it, including the underdetermination generated by the multiplicity of formulations and interpretations of quantum physics, each presenting a different way the world could be. Authors in this volume offer a range of alternative ways forward: some suggest new articulations of realism, limiting our commitments in one way or another; others attempt to articulate a ‘third way’ between traditional forms of realism and antirealism, or are critical of such attempts. Still others argue that quantum theory itself should be reconceptualised, or at least alternative formulations should be considered in the hope of evading the problems faced by realism. And some examine the nature of these issues when moving beyond quantum mechanics to quantum field theory. Taken together they offer an exciting new set of perspectives on one of the most fundamental questions in the philosophy of modern physics: how can one be a realist about quantum theory, and what does this realism amount to?

scholarly journals Entanglement and Phase-Mediated Correlations in Quantum Field Theory. Application to Brain-Mind States

2019 ◽  
Vol 9 (15) ◽  
pp. 3203 ◽  
Author(s):  
Shantena A. Sabbadini ◽  
Giuseppe Vitiello
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Optics ◽  
Quantum Model ◽  
Observational Methods ◽  
Quantum Field ◽  
Theory Application ◽  
The Brain

The entanglement phenomenon plays a central role in quantum optics and in basic aspects of quantum mechanics and quantum field theory. We review the dissipative quantum model of brain and the role of the entanglement in the brain-mind activity correlation and in the formation of assemblies of coherently-oscillating neurons, which are observed to appear in different regions of the cortex by use of EEG, ECoG, fNMR, and other observational methods in neuroscience.

Quantum gravity

1979 ◽  
Vol 368 (1732) ◽  
pp. 33-36
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Theory ◽  
Asymptotic Freedom ◽  
Quantum Field ◽  
Yang Mills ◽  
Black Hole Background ◽  
New Ideas

The nature of the search for a quantum theory of gravity has undergone significant changes over the last few years. This is partly because the success of renormalized Yang-Mills gauge theory has stimulated interest in quantum field theory leading to a number of new ideas (for example instantons, solitons, monopoles, asymptotic freedom) which, focusing as they do on non-perturbative aspects, are potentially of considerable importance in a gravitational context. There has also been the development of supersymmetry and the associated supergravity theories for which the prognosis for quantization is brighter than normal General Relativity. Finally, a major impact was made by Hawking’s (1975) discovery of the thermal radiation produced when a quantum field propagates in a black hole background. This leads to a remarkable synthesis of thermodynamics, quantum theory and general relativity whose significance for physics has still not yet been fully explored. Traditionally, the methods for quantizing the gravitational field have been divided into ‘canonical’ and ‘covariant’ (Isham et al. 1975). A number of years ago the main attack on the canonical front was the quantization of the classical constraints

scholarly journals AN ATTEMPT TOWARDS FIELD THEORY OF D0 BRANES — QUANTUM M-FIELD THEORY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2343-2351 ◽  
Author(s):  
TAMIAKI YONEYA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Recent Attempt ◽  
Bilinear Forms ◽  
Quantum Field ◽  
New Formalism ◽  
Yang Mills ◽  
Large N ◽  
New Framework

I discuss my recent attempt in search of a new framework for quantum field theory of D branes. After explaining some motivations in the background of this project, I present, as a first step towards our goal, a second-quantized reformulation of the U (N) Yang-Mills quantum mechanics in which the D0-brane creation-and-annihilation fields connecting theories with different N are introduced. Physical observables are expressed in terms of bilinear forms of the D0 fields. The large N limit is briefly treated using this new formalism.

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

scholarly journals ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

2006 ◽  
Vol 03 (07) ◽  
pp. 1303-1312 ◽  
Author(s):  
WEIGANG QIU ◽  
FEI SUN ◽  
HONGBAO ZHANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Casimir Effect ◽  
Minkowski Spacetime ◽  
Quantum Field ◽  
Explicit Result ◽  
Massless Spin ◽  
The Many ◽  
The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

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