scholarly journals Boundary Conditions that Remove Certain Ultraviolet Divergences

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 577
Author(s):  
Roderich Tumulka
Keyword(s):  
Boundary Condition ◽  
Wave Function ◽  
Boundary Conditions ◽  
Particle Creation ◽  
Quantum Field ◽  
Interior Boundary ◽  
Direct Definition ◽  
Definition Of ◽  
Particle Creation And Annihilation ◽  
Interior Boundary Conditions

In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and by taking limits in which a UV cutoff tends toward infinity. Here, I review a novel way of removing UV divergences: by imposing a type of boundary condition on the wave function. These conditions, called interior-boundary conditions (IBCs), relate the values of the wave function at two configurations linked by the creation or annihilation of a particle. They allow for a direct definition of the Hamiltonian without renormalization or limiting procedures. In the last section, I review another boundary condition that serves to determine the probability distribution of detection times and places on a time-like 3-surface.

scholarly journals Multi-time formulation of particle creation and annihilation via interior-boundary conditions

2019 ◽  
Vol 32 (02) ◽  
pp. 2050004 ◽  
Author(s):  
Matthias Lienert ◽  
Lukas Nickel
Keyword(s):  
Boundary Conditions ◽  
Fock Space ◽  
Lorentz Invariance ◽  
Particle Creation ◽  
Wave Functions ◽  
Constant Matrix ◽  
Relativistic Case ◽  
Interior Boundary ◽  
Particle Creation And Annihilation ◽  
Interior Boundary Conditions

Interior-boundary conditions (IBCs) have been suggested as a possibility to circumvent the problem of ultraviolet divergences in quantum field theories. In the IBC approach, particle creation and annihilation is described with the help of linear conditions that relate the wave functions of two sectors of Fock space: [Formula: see text] at an interior point [Formula: see text] and [Formula: see text] at a boundary point [Formula: see text], typically a collision configuration. Here, we extend IBCs to the relativistic case. To do this, we make use of Dirac’s concept of multi-time wave functions, i.e. wave functions [Formula: see text] depending on [Formula: see text] space-time coordinates [Formula: see text] for [Formula: see text] particles. This provides the manifestly covariant particle-position representation that is required in the IBC approach. In order to obtain rigorous results, we construct a model for Dirac particles in 1+1 dimensions that can create or annihilate each other when they meet. Our main results are an existence and uniqueness theorem for that model, and the identification of a class of IBCs ensuring local probability conservation on all Cauchy surfaces. Furthermore, we explain how these IBCs relate to the usual formulation with creation and annihilation operators. The Lorentz invariance is discussed and it is found that, apart from a constant matrix (which is required to transform in a certain way), the model is manifestly Lorentz invariant. This makes it clear that the IBC approach can be made compatible with relativity.

scholarly journals The dissipative approach to quantum field theory: conceptual foundations and ontological implications

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrea Oldofredi ◽  
Hans Christian Öttinger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Nonequilibrium Thermodynamics ◽  
Particle Creation ◽  
Mathematical Structure ◽  
Alternative Formulation ◽  
Quantum Field ◽  
Conceptual Foundations ◽  
Particle Creation And Annihilation

AbstractMany attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the dissipative approach to QFT, a new alternative formulation of the theory explaining the phenomena of particle creation and annihilation starting from nonequilibrium thermodynamics. It is shown that DQFT presents a rigorous mathematical structure, and a clear particle ontology, taking the best from the mentioned perspectives. Finally, after the discussion of its principal implications and consequences, we compare it with the main Bohmian QFTs implementing a particle ontology.

ANYON EQUATION ON A TORUS

1992 ◽  
Vol 07 (23) ◽  
pp. 5797-5831 ◽  
Author(s):  
CHOON-LIN HO ◽  
YUTAKA HOSOTANI
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Essential Role ◽  
Wilson Line ◽  
Regular Function ◽  
Gauge Fields ◽  
Quantum Field ◽  
Many Body ◽  
Definition Of ◽  
Chern Simons

Starting from the quantum field theory of nonrelativistic matter on a torus interacting with Chern-Simons gauge fields, we derive the Schrödinger equation for an anyon system. The nonintegrable phases of the Wilson line integrals on a torus play an essential role. In addition to generating degenerate vacua, they enter in the definition of a many-body Schrödinger wave function in quantum mechanics, which can be defined as a regular function of the coordinates of anyons. It obeys a non-Abelian representation of the braid group algebra, being related to Einarsson’s wave function by a singular gauge transformation.

scholarly journals Classifying boundary conditions in JT gravity: from energy-branes to α-branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Akash Goel ◽  
Luca V. Iliesiu ◽  
Jorrit Kruthoff ◽  
Zhenbin Yang
Keyword(s):  
Boundary Condition ◽  
Black Holes ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Ensemble Averaging ◽  
Matrix Integral ◽  
Two Dimensional Model ◽  
Definition Of ◽  
Extremal Black Holes

Abstract We classify the possible boundary conditions in JT gravity and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties and ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and, finally, its role as a two-dimensional model of cosmology.

Hydrodynamic Regimes, Knudsen Layer, Numerical Schemes: Definition of Boundary Fluxes

2011 ◽  
Vol 3 (5) ◽  
pp. 519-561 ◽  
Author(s):  
Christophe Besse ◽  
Saja Borghol ◽  
Thierry Goudon ◽  
Ingrid Lacroix-Violet ◽  
Jean-Paul Dudon
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Conservation Laws ◽  
Numerical Solution ◽  
Boundary Layers ◽  
Mean Free Path ◽  
Euler System ◽  
Knudsen Layer ◽  
Microscopic Modeling ◽  
Definition Of

AbstractWe propose a numerical solution to incorporate in the simulation of a system of conservation laws boundary conditions that come from a microscopic modeling in the small mean free path regime. The typical example we discuss is the derivation of the Euler system from the BGK equation. The boundary condition relies on the analysis of boundary layers formation that accounts from the fact that the incoming kinetic flux might be far from the thermodynamic equilibrium.

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