scholarly journals UTILITY OF GALILEAN SYMMETRY IN LIGHT-FRONT PERTURBATION THEORY: A NONTRIVIAL EXAMPLE IN QCD

1998 ◽  
Vol 13 (26) ◽  
pp. 4591-4604 ◽  
Author(s):  
A. HARINDRANATH ◽  
RAJEN KUNDU
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Complex Structure ◽  
Light Front ◽  
Tree Level ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Two Component ◽  
Covariant Field ◽  
Galilean Symmetry

Investigations have revealed a very complex structure for the coefficient functions accompanying the divergences for individual time(x+)-ordered diagrams in light-front perturbation theory. No guidelines seem to be available to look for possible mistakes in the structure of these coefficient functions emerging at the end of a long and tedious calculation, in contrast to covariant field theory. Since, in light-front field theory, the transverse boost generator is a kinematical operator which acts just like the two-dimensional Galilean boost generator in nonrelativistic dynamics, it may provide some constraint on the resulting structures. In this work we investigate the utility of Galilean symmetry beyond tree level in the context of coupling constant renormalization in light-front QCD using the two-component formalism. We show that for each x+-ordered diagram separately, the underlying transverse boost symmetry fixes relative signs of terms in the coefficient functions accompanying the diverging logarithms. We also summarize the results leading to coupling constant renormalization for the most general kinematics.

Light front field theory: An advanced Primer

2007 ◽  
Vol 57 (3) ◽  
Author(s):  
L'ubomír Martinovič
Keyword(s):  
Field Theory ◽  
Detailed Comparison ◽  
Light Front ◽  
Two Dimensional ◽  
Schwinger Model ◽  
Initial Space ◽  
Model Hamiltonian ◽  
Spatial Volume ◽  
Hamiltonian Perturbation Theory ◽  
Light Front Quantization

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

An exactly solvable two component classical Coulomb system

1984 ◽  
Vol 26 (2) ◽  
pp. 119-128 ◽  
Author(s):  
Peter J. Forrester
Keyword(s):  
Coulomb Potential ◽  
Correlation Functions ◽  
Asymptotic Form ◽  
Coulomb System ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Sum Rule ◽  
Exactly Solvable ◽  
Two Component ◽  
Special Value

AbstractA two component classical Coulomb system is considered, in which particles of charge +q and + 2q are constrained to lie on a circle and interact via the two-dimensional Coulomb potential. At a special value of the coupling constant the correlation functions are calculated exactly and the asymptotic form of the truncated charge-charge correlation is found to obey Jancovici's sum rule.

scholarly journals OPEN-CLOSED DUALITY: LESSONS FROM MATRIX MODEL

2004 ◽  
Vol 19 (11) ◽  
pp. 841-853 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Matrix Model ◽  
String Field Theory ◽  
Classical Result ◽  
Open String ◽  
Closed String ◽  
Tree Level ◽  
Two Dimensional

Recent investigations involving the decay of unstable D-branes in string theory suggest that the tree level open string theory which describes the dynamics of the D-brane already knows about the closed string states produced in the decay of the brane. We propose a specific conjecture involving quantum open string field theory to explain this classical result, and show that the recent results in two-dimensional string theory are in exact accordance with this conjecture.

scholarly journals g-FUNCTION IN PERTURBATION THEORY

2004 ◽  
Vol 19 (15) ◽  
pp. 2545-2559
Author(s):  
ANATOLY KONECHNY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Beta Function ◽  
Open String ◽  
Quantum Field ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
The Given

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disk. The form of the potential function and metric that we consider were introduced in Refs. 16 and 18 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.

scholarly journals BRST COHOMOLOGY IN BELTRAMI PARAMETRIZATION

1996 ◽  
Vol 11 (02) ◽  
pp. 375-393 ◽  
Author(s):  
LIVIU TĂTARU ◽  
ION V. VANCEA
Keyword(s):  
Field Theory ◽  
Riemann Surface ◽  
Complex Structure ◽  
Theory Model ◽  
Two Dimensional ◽  
Field Theory Model ◽  
Scalar Matter ◽  
Brst Cohomology ◽  
Lagrangian Field Theory ◽  
Matter Fields

We study the BRST cohomology within a local conformal Lagrangian field theory model built on a two-dimensional Riemann surface with no boundary. We deal with the case of the complex structure parametrized by the Beltrami differential and the scalar matter fields. The computation of all elements of the BRST cohomology is given.

scholarly journals Singular structure of the QED effective action

2019 ◽  
Vol 49 ◽  
pp. 1960006
Author(s):  
B. A. Fayzullaev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Singular Perturbation ◽  
Effective Action ◽  
Electromagnetic Interaction ◽  
Perturbation Series ◽  
Singular Perturbation Theory ◽  
Quantum Field ◽  
Coupling Constant

The equations for the QED effective action derived in Ref. 3 are considered using singular perturbation theory. The effective action is divided into regular and singular (in coupling constant) parts. It is shown that expression for the regular part coincides with usual Feynman perturbation series over coupling constant, while the remainder has essential singularity at the vanishing coupling constant: [Formula: see text]. This means that in the frame of quantum field theory it is impossible “to switch off” electromagnetic interaction in general and pass on to “free electron”.

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