The Principles of Quantum Theory, Dirac’s Equation, and the Architecture of Quantum Field Theory

2016 ◽  
pp. 207-246
Author(s):  
Arkady Plotnitsky
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Quantum Field

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.

On the Calculation of Nonlinear Spinor Field Functionals

1971 ◽  
Vol 26 (4) ◽  
pp. 623-630 ◽  
Author(s):  
H Stumpf
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Spinor Field ◽  
Functional Equations ◽  
High Energy ◽  
Quantum Field ◽  
Nonlinear Spinor ◽  
Physical Problems ◽  
Physical Information

Abstract Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory one has to describe the physical information by functional operations only. Such operations have been defined in preceding papers. To apply these operations to physical problems, the corresponding functionals have to be known. Therefore in this paper calculational procedures for functionals are discussed. As high energy phenomena are of interest, the calculational procedures are given for spinor field functionals. Especially a method for the calculation of stationary and Fermion-Fermion scattering functionals is proposed.

scholarly journals Lorentzian quantum reality: postulates and toy models

2015 ◽  
Vol 373 (2047) ◽  
pp. 20140241 ◽  
Author(s):  
Adrian Kent
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Minkowski Space ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Relativistic Quantum Theory ◽  
Quantum Reality ◽  
Background Space

We describe postulates for a novel realist version of relativistic quantum theory or quantum field theory in Minkowski space and other background space–times, and illustrate their application with toy models.

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.

KOLMOGOROV SYSTEMS AND ANOSOV SYSTEMS IN QUANTUM THEORY

2001 ◽  
Vol 04 (01) ◽  
pp. 85-119 ◽  
Author(s):  
H. NARNHOFER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Quantum Field ◽  
Modular Systems ◽  
One Dimensional ◽  
Classical Systems ◽  
Anosov Systems

In analogy to classical systems, quantum K-systems and quantum Anosov systems are defined. Their relation especially for modular systems is discussed as well as the consequences on clustering properties. Examples for such systems in the framework of quantum field theory and one-dimensional theories are offered.

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?

Functional Quantum Theory of Free Relativistic Scalar Fields

1971 ◽  
Vol 26 (9) ◽  
pp. 1553-1558 ◽  
Author(s):  
W. Bauhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Functional Equations ◽  
Scalar Product ◽  
Functional Space ◽  
Scalar Fields ◽  
Quantum Field ◽  
Isometric Mapping ◽  
Free Scalar

Abstract Dynamics of quantum field theory can be formulated by functional equations. Starting with the Schwinger functionals of the free scalar field, functional equations and corresponding many particle functionals are derived. To establish a complete functional quantum theory, a scalar product in functional space has to be defined as an isometric mapping of physical Hilbert space into the functional space.

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