scholarly journals Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Qiang Chen ◽  
Jianyuan Xiao ◽  
Peifeng Fan
Keyword(s):  
Field Theory ◽  
Real Time ◽  
Quantum Electrodynamics ◽  
Symplectic Form ◽  
Strong Field ◽  
Relativistic Quantum ◽  
High Order ◽  
High Quality ◽  
Geometric Structures ◽  
Gauge Invariant

Abstract A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic quantum plasmas (RQP) phenomena. With minimal coupling, the Lagrangian density of an interacting bispinor-gauge fields theory is constructed in a conjugate real fields form. The canonical symplectic form and canonical equations of this field theory are obtained by the general Hamilton’s principle on cotangent bundle. Based on discrete exterior calculus, the gauge field components are discreted to form a cochain complex, and the bispinor components are naturally discreted on a staggered dual lattice as combinations of differential forms. With pull-back and push-forward gauge covariant derivatives, the discrete action is gauge invariant. A well-defined discrete canonical Poisson bracket generates a semi-discrete lattice canonical field theory (LCFT), which admits the canonical symplectic form, unitary property, gauge symmetry and discrete Poincaré subgroup, which are good approximations of the original continuous geometric structures. The Hamiltonian splitting method, Cayley transformation and symmetric composition technique are introduced to construct a class of high-order numerical schemes for the semi-discrete LCFT. These schemes involve two degenerate fermion flavors and are locally unconditional stable, which also preserve the geometric structures. Admitting Nielsen-Ninomiya theorem, the continuous chiral symmetry is partially broken on the lattice. As an extension, a pair of discrete chiral operators are introduced to reconstruct the lattice chirality. Equipped with statistically quantization-equivalent ensemble models of the Dirac vacuum and non-trivial plasma backgrounds, the schemes are expected to have excellent performance in secular simulations of relativistic quantum effects, where the numerical errors of conserved quantities are well bounded by very small values without coherent accumulation. The algorithms are verified in detail by numerical energy spectra. Real-time LCFT simulations are successfully implemented for the nonlinear Schwinger mechanism induced e-e+ pairs creation and vacuum Kerr effect, where the nonlinear and non-perturbative features captured by the solutions provide a complete strong-field physical picture in a very wide range, which open a new door toward high-quality simulations in SFQED and RQP fields.

scholarly journals Type II superstring field theory with cyclic $L_\infty$ structure

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
H Kunimoto ◽  
T Sugimoto
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
String Field Theory ◽  
Symplectic Form ◽  
Closed String ◽  
Type Ii ◽  
Gauge Invariant ◽  
Non Local ◽  
String Amplitudes ◽  
Algebraic Formulation

Abstract We construct a complete type II superstring field theory that includes all the NS–NS, R–NS, NS–R, and R–R sectors. As in the open and heterotic superstring cases, the R–NS, NS–R, and R–R string fields are constrained by using the picture-changing operators. In particular, we use a non-local inverse picture-changing operator for the constraint on the R–R string field, which seems to be inevitable due to the compatibility of the extra constraint with the closed string constraints. The natural symplectic form in the restricted Hilbert space gives a non-local kinetic action for the R–R sector, but it correctly provides the propagator expected from the first-quantized formulation. Extending the prescription previously obtained for the heterotic string field theory, we give a construction of general type II superstring products, which realizes a cyclic $L_\infty$ structure, and thus provides a gauge-invariant action based on the homotopy algebraic formulation. Three typical four-string amplitudes derived from the constructed string field theory are demonstrated to agree with those in the first-quantized formulation. We also give the half-Wess–Zumino–Witten action defined in the medium Hilbert space whose left-moving sector is still restricted to the small Hilbert space.

Simplifying calculations in real time finite temperature field theory

2007 ◽  
Vol 85 (6) ◽  
pp. 671-677
Author(s):  
T Fugleberg ◽  
M E Carrington
Keyword(s):  
Field Theory ◽  
Temperature Field ◽  
Real Time ◽  
Finite Temperature ◽  
Quantum Electrodynamics ◽  
Previous Experience ◽  
Ward Identities ◽  
Finite Temperature Field Theory ◽  
Time Path ◽  
11.10 Wx

In this paper, we discuss a Mathematica program that we have written that calculates the integrand for amplitudes in the closed-time-path formulation of real-time finite-temperature field theory. The program is designed to be used by someone with no previous experience with Mathematica. It performs contractions over tensor indices that appear in real-time finite-temperature field theory and gives the result in the 1-2, Keldysh or R/A basis. As an illustration of this program, we discuss the calculation of all 3-point ward identities in finite-temperature quantum electrodynamics with full vertices. PACS Nos.: 11.10.Wx,11.15.-q

scholarly journals Path Integral based Non-equilibrium Quantum Field Theory of Non-relativistic Pairs inside an Environment

2021 ◽  
Author(s):  
Tobias Binder
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Differential Equations ◽  
Path Integral ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Einstein Condensation ◽  
Full Potential ◽  
Quantum Field ◽  
Non Equilibrium

Abstract We derive differential equations from path integral based non-equilibrium quantum field theory, that cover the dynamics and spectrum of non-relativistic two-body fields for any environment. For concreteness of the two-body fields, we choose the full potential non-relativistic Quantum Electrodynamics Lagrangian in this work. After closing the correlation function hierarchy of these differential equations and performing consistency checks with previous literature under certain limits, we demonstrate the range of physics applications. This includes Cosmology such as Dark Matter in the primordial plasma, Quarkonia Physics inside a quark-gluon plasma, and Condensed and strongly Correlated Matter Physics such as Bose-Einstein condensation or Superconductivity. Since we always had to take limits or approximations of our equations in order to recover those known cases, our equations could contain new phenomena. In particular they are based on non-equilibrium Green's function that can deal with non-hermite potentials as well as dynamical formation of different extreme phases. We propose a scheme for other Lagrangian based theories or higher N-body states such as molecules to derive analogous equations.

The neutral relativistic scalar field

2021 ◽  
pp. 105-124
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Real Time ◽  
Statistical Physics ◽  
Relativistic Quantum ◽  
Pair Potential ◽  
Field Extension ◽  
Bose Gas ◽  
Real Field ◽  
Relativistic Limit ◽  
Grand Canonical

This chapter introduces the relativistic quantum field theory (QFT) of the neutral scalar boson field. It is a local, relativistic invariant, theory for a real field extension of the non-relativistic field theory of the Bose gas. Locality is a property that plays a central role in most of this work. The QFT is discussed both from the viewpoint of real-time evolution and statistical physics. The holomorphic formalism leads to representations of the S-matrix in terms of field integrals. The S-matrix elements are related to the continuation to real time of various kinds of Euclidean correlation functions. It is argued that the massive φ4 QFT has the quantum Bose gas with a pair potential, in the grand canonical formulation, as a non-relativistic limit.

Relativistic Quantum Fields

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Scattering Theory ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Quantum Fields ◽  
Formal Expression ◽  
Feynman Rules ◽  
Wightman Axioms

The general formulation of quantum field theory. The Wightman axioms. The PCT and spin-statistics theorems. The assumption for the existence of asymptotic states. The reduction formulae and scattering theory. The Feynman rules for the S-matrix. Discussion for spin-12 and spin-1 particles. Applications to quantum electrodynamics. A formal expression for the S-matrix.

scholarly journals An introduction to NRQED

2015 ◽  
Vol 30 (26) ◽  
pp. 1550128 ◽  
Author(s):  
Gil Paz
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Cross Section ◽  
Effective Field Theory ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Thomson Scattering ◽  
Effective Field ◽  
Low Energy ◽  
Sample Application

We present a pedagogical introduction to NRQED (non-relativistic quantum electrodynamics). NRQED is an effective field theory that describes the interaction of non-relativistic, possibly composite, spin- [Formula: see text] particle with the electromagnetic field. We explain in detail how the NRQED Lagrangian is constructed up to and including order [Formula: see text], where M is the mass of the spin- [Formula: see text] particle. As a sample application, we derive the Thomson scattering cross-section for the low energy scattering of a photon and a possibly composite spin- [Formula: see text] particle.

Sky Segmentation for Enhanced Depth Reconstruction and Bokeh Rendering with Efficient Architectures

2020 ◽  
Vol 2020 (14) ◽  
pp. 378-1-378-7
Author(s):  
Tyler Nuanes ◽  
Matt Elsey ◽  
Radek Grzeszczuk ◽  
John Paul Shen
Keyword(s):  
Real Time ◽  
Mobile Device ◽  
Computational Cost ◽  
False Positives ◽  
Compact Model ◽  
High Quality ◽  
False Negatives ◽  
Trade Off ◽  
Depth Reconstruction ◽  
Binary Classifiers

We present a high-quality sky segmentation model for depth refinement and investigate residual architecture performance to inform optimally shrinking the network. We describe a model that runs in near real-time on mobile device, present a new, highquality dataset, and detail a unique weighing to trade off false positives and false negatives in binary classifiers. We show how the optimizations improve bokeh rendering by correcting stereo depth misprediction in sky regions. We detail techniques used to preserve edges, reject false positives, and ensure generalization to the diversity of sky scenes. Finally, we present a compact model and compare performance of four popular residual architectures (ShuffleNet, MobileNetV2, Resnet-101, and Resnet-34-like) at constant computational cost.

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.

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