Projection operators in quantum theory of relativistic free fields

1967 ◽  
Vol 51 (1) ◽  
pp. 14-39 ◽  
Author(s):  
A. Aurilia ◽  
H. Umezawa
Keyword(s):  
Quantum Theory ◽  
Projection Operators ◽  
Free Fields

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

Quantum Theory of Non-Local Fields. Part I. Free Fields

1950 ◽  
Vol 77 (2) ◽  
pp. 219-226 ◽  
Author(s):  
Hideki Yukawa
Keyword(s):  
Quantum Theory ◽  
Local Fields ◽  
Non Local ◽  
Free Fields

The Quantum Theory of Free Fields

2010 ◽  
pp. 109-149
Author(s):  
Henryk Arodź ◽  
Dr. Leszek Hadasz
Keyword(s):  
Quantum Theory ◽  
Free Fields

Quantum Theory

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Quantum Theory ◽  
Mathematical Representation ◽  
General Notion ◽  
Projection Operators ◽  
Statistical Independence ◽  
Level System ◽  
Mixed States ◽  
Macroscopic System ◽  
Composite Systems ◽  
System A

From the outset statistical mechanics will be framed in the language of quantum theory. The typical macroscopic system is composed of multiple constituents, and hence described in some many-particle Hilbert space. In general, not much is known about such a system, certainly not the precise preparation of all its microscopic details. Thus, its description requires a more general notion of a quantum state, a so-called mixed state. This chapter begins with a brief review of the basic axioms of quantum theory regarding observables, pure states, measurements, and time evolution. Particular attention is paid to the use of projection operators and to the most elementary quantum system, a two-level system. The chapter then motivates the introduction of mixed states and examines in detail their mathematical representation and properties. It also dwells on the description of composite systems, introducing, in particular, the notions of statistical independence and correlations.

scholarly journals Acausal quantum theory for non-Archimedean scalar fields

2019 ◽  
Vol 31 (04) ◽  
pp. 1950011 ◽  
Author(s):  
M. L. Mendoza-Martínez ◽  
J. A. Vallejo ◽  
W. A. Zúñiga-Galindo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Scalar Fields ◽  
Background Field ◽  
Quantum Field ◽  
Second Quantization ◽  
Klein Gordon ◽  
Free Fields ◽  
Wightman Axioms

We construct a family of quantum scalar fields over a [Formula: see text]-adic spacetime which satisfy [Formula: see text]-adic analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the same way for both the Archimedean and non-Archimedean frameworks; however, the axioms depending on the ordering of the background field must be reformulated, reflecting the acausality of [Formula: see text]-adic spacetime. The [Formula: see text]-adic scalar fields satisfy certain [Formula: see text]-adic Klein–Gordon pseudo-differential equations. The second quantization of the solutions of these Klein–Gordon equations corresponds exactly to the scalar fields introduced here. The main conclusion is that there seems to be no obstruction to the existence of a mathematically rigorous quantum field theory (QFT) for free fields in the [Formula: see text]-adic framework, based on an acausal spacetime.

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