scholarly journals Classical simulation of quantum fields I

2006 ◽  
Vol 84 (10) ◽  
pp. 861-877 ◽  
Author(s):  
T Hirayama ◽  
B Holdom
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Zero Point ◽  
Background Field ◽  
Field Configuration ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Point Energy ◽  
Classical Simulation ◽  
Feynman Rules

We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical electrodynamics by Wheeler–Feynman and the theory of stochastic electrodynamics of Boyer. The nonperturbative effects of interactions in these theories can be very efficiently studied on the lattice. In [Formula: see text] theory in 1 + 1 dimensions, we find results, in particular, for mass renormalization and the critical coupling for symmetry breaking that are in agreement with their quantum counterparts. We then study the perturbative expansion of the n-point Green's functions and find a loop expansion very similar to that of quantum field theory. When compared to the usual Feynman rules, we find some differences associated with particular combinations of internal lines going on-shell simultaneously. PACS Nos.: 03.70.+k, 03.50.–z, 11.15.Tk

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

Interacting Fields

2021 ◽  
pp. 237-252
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Expansion ◽  
Field Theories ◽  
Green Functions ◽  
Quantum Field ◽  
Minkowski Space Time ◽  
Dimensional Minkowski Space ◽  
Feynman Rules ◽  
Wightman Axioms

We present a simple form of the Wightman axioms in a four-dimensional Minkowski space-time which are supposed to define a physically interesting interacting quantum field theory. Two important consequences follow from these axioms. The first is the invariance under CPT which implies, in particular, the equality of masses and lifetimes for particles and anti-particles. The second is the connection between spin and statistics. We give examples of interacting field theories and develop the perturbation expansion for Green functions. We derive the Feynman rules, both in configuration and in momentum space, for some simple interacting theories. The rules are unambiguous and allow, in principle, to compute any Green function at any order in perturbation.

Electrodynamics

2018 ◽  
Author(s):  
James T. Cushing
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Physical Theory ◽  
Special Theory ◽  
Classical Electrodynamics ◽  
Quantum Field ◽  
Theory Of Relativity ◽  
Electric And Magnetic Fields ◽  
Fundamental Physical

Electric charges interact via the electric and magnetic fields they produce. Electrodynamics is the study of the laws governing these interactions. The phenomena of electricity and of magnetism were once taken to constitute separate subjects. By the beginning of the nineteenth century they were recognized as closely related topics and by the end of that century electromagnetic phenomena had been unified with those of optics. Classical electrodynamics provided the foundation for the special theory of relativity, and its unification with the principles of quantum mechanics has led to modern quantum field theory, arguably our most fundamental physical theory to date.

scholarly journals A quest for a “direct” observation of the Unruh effect with classical electrodynamics: In honor of Atsushi Higuchi 60th anniversary

2018 ◽  
Vol 27 (11) ◽  
pp. 1843008 ◽  
Author(s):  
Gabriel Cozzella ◽  
André G. S. Landulfo ◽  
George E. A. Matsas ◽  
Daniel A. T. Vanzella
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Direct Observation ◽  
Linear Acceleration ◽  
Classical Electrodynamics ◽  
Unruh Effect ◽  
Quantum Field ◽  
Simple Experiment ◽  
60Th Anniversary ◽  
Accelerated Frames

The Unruh effect is essential to keep the consistency of quantum field theory in inertial and uniformly accelerated frames. Thus, the Unruh effect must be considered as well-tested as quantum field theory itself. In spite of it, it would be nice to realize an experiment whose output could be directly interpreted in terms of the Unruh effect. This is not easy because the linear acceleration needed to reach a temperature of 1[Formula: see text]K is of order [Formula: see text]. We discuss here a conceptually simple experiment reachable under present technology, which may accomplish this goal. The inspiration for this proposal can be traced back to Atsushi Higuchi’s Ph.D. thesis, which makes it particularly suitable to pay tribute to him on occasion of his [Formula: see text]th anniversary.

Quantum field theory in phase space

2019 ◽  
Vol 34 (08) ◽  
pp. 1950037 ◽  
Author(s):  
R. G. G. Amorim ◽  
F. C. Khanna ◽  
A. P. C. Malbouisson ◽  
J. M. C. Malbouisson ◽  
A. E. Santana
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Phase Space ◽  
Relativistic Quantum ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Feynman Rules ◽  
Klein Gordon ◽  
Quantization Rules

The tilde conjugation rule in thermofield dynamics, equivalent to the modular conjugation in a [Formula: see text]-algebra, is used to develop unitary representations of the Poincaré group, where the Hilbert space has the phase space content, a symplectic Hilbert space. The state is described by a quasi-amplitude of probability, which is a sort of wave function in phase space, associated with the Wigner function. The quantum field theory in phase space is then constructed, including the quantization rules for the Klein–Gordon and the Dirac fields, the derivation of the electrodynamics in phase space and elements of a relativistic quantum kinetic theory. Towards a physical interpretation of the theory, propagators are associated with the corresponding Wigner functions. The Feynman rules follow accordingly with vertices similar to those of usual non-Abelian quantum field theories.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points.  Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques  (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to  n > 3  in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. On the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighboring space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

scholarly journals Emerging Quantum Fields Embedded in the Emergence of Spacetime

2018 ◽  
Author(s):  
Hans Diel
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Causal Model ◽  
Space Time ◽  
Quantum Field ◽  
Quantum Fields ◽  
Standard Quantum ◽  
Discrete Spacetime ◽  
Feynman Rules ◽  
Space Point

Based on a local causal model of the dynamics of curved discrete spacetime, a causal model of quantum field theory in curved discrete spacetime is described. At the elementary level, space(-time) is assumed to consists of interconnected space points. Each space point is connected to a small discrete set of neighbor space points. Density distribution of the space points and the lengths of the space point connections depend on the distance from the gravitational sources. This leads to curved spacetime in accordance with general relativity. Dynamics of spacetime (i.e., the emergence of space and the propagation of space changes) dynamically assigns "in-connections" and "out-connections" to the affected space points. Emergence and propagation of quantum fields (including particles) are mapped to the emergence and propagation of space changes by utilizing identical paths of in/out-connections. Compatibility with standard quantum field theory (QFT) requests the adjustment of the QFT techniques (e.g., Feynman diagrams, Feynman rules, creation/annihilation operators), which typically apply to three in/out connections, to n > 3 in/out connections. In addition, QFT computation in position space has to be adapted to a curved discrete space-time.

Dynamical derivation of the Yang–Mills S-matrix

1982 ◽  
Vol 60 (11) ◽  
pp. 1630-1640
Author(s):  
Robert E. Pugh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Matrix Equation ◽  
Quantum Field ◽  
Yang Mills ◽  
Covariant Quantum ◽  
S Matrix ◽  
Feynman Rules

The Feynman rules for self-interacting Yang–Mills fields are derived within the framework of conventional covariant quantum field theory by explicitly calculating the contributions of the nonphysical field components to the violations of the S-matrix equation of continuity.

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