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 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.

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 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.

Hyper-asymptotic expansions and instantons

2019 ◽  
pp. 471-492
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Asymptotic Expansions ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
Wkb Method ◽  
Additional Information ◽  
Spectral Equation ◽  
Double Well Potential

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by quantum barrier penetration effects. The analysis of the large order behaviour, based on instanton calculus, shows that the perturbative expansion is not Borel summable, and does not define unique functions. An important issue is then what kind of additional information is required to determine the exact expanded functions. While the QFT examples are complicated, and their study is still at the preliminary stage, in quantum mechanics, in the case of some analytic potentials that have degenerate minima (like the quartic double–well potential), the problem has been completely solved. Some examples are described in Chapter 24. There, the perturbative, complete, hyper–asymptotic expansion exhibits the resurgence property. The perturbative expansion can be related to the calculation of the spectral equation via the complex WKB method.

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