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Title: Multi-time wave functions for quantum field theory

Abstract

Multi-time wave functions such as ϕ(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wavemore » functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.« less

Authors:
 [1];  [2]
  1. Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München (Germany)
  2. Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States)
Publication Date:
OSTI Identifier:
22314818
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 345; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; CREATION OPERATORS; HEISENBERG PICTURE; QUANTUM FIELD THEORY; QUANTUM MECHANICS; QUANTUM STATES; RELATIVISTIC RANGE; SCHROEDINGER EQUATION; SPACE-TIME; VECTORS; WAVE FUNCTIONS

Citation Formats

Petrat, Sören, and Tumulka, Roderich. Multi-time wave functions for quantum field theory. United States: N. p., 2014. Web. doi:10.1016/J.AOP.2014.03.004.
Petrat, Sören, & Tumulka, Roderich. Multi-time wave functions for quantum field theory. United States. https://doi.org/10.1016/J.AOP.2014.03.004
Petrat, Sören, and Tumulka, Roderich. 2014. "Multi-time wave functions for quantum field theory". United States. https://doi.org/10.1016/J.AOP.2014.03.004.
@article{osti_22314818,
title = {Multi-time wave functions for quantum field theory},
author = {Petrat, Sören and Tumulka, Roderich},
abstractNote = {Multi-time wave functions such as ϕ(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.},
doi = {10.1016/J.AOP.2014.03.004},
url = {https://www.osti.gov/biblio/22314818}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = Complete,
volume = 345,
place = {United States},
year = {Sun Jun 15 00:00:00 EDT 2014},
month = {Sun Jun 15 00:00:00 EDT 2014}
}