scholarly journals Field theory of disordered elastic interfaces at 3-loop order: The β-function

2018 ◽  
Vol 932 ◽  
pp. 540-588 ◽  
Author(s):  
Kay Jörg Wiese ◽  
Christoph Husemann ◽  
Pierre Le Doussal
Keyword(s):  
Field Theory ◽  
Loop Order ◽  
Elastic Interfaces ◽  
Β Function

scholarly journals A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 956
Author(s):  
Dafne Carolina Arias-Perdomo ◽  
Adriano Cherchiglia ◽  
Brigitte Hiller ◽  
Marcos Sampaio
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Symmetry ◽  
Particle Physics ◽  
Analytic Extension ◽  
Quantum Field ◽  
Loop Order ◽  
Time Dimension ◽  
The Core ◽  
Striking Success

Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order. We also pedagogically discuss how the method complies with gauge symmetry using one- and two-loop examples in QED and QCD.

Evaluation of loop diagrams using quantum mechanics

1992 ◽  
Vol 70 (8) ◽  
pp. 652-655 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Matrix Element ◽  
Proper Time ◽  
Quantum Field ◽  
Loop Momentum ◽  
Loop Order ◽  
Point Function ◽  
Integral Formalism ◽  
Time Formalism

In using the proper time formalism, Schwinger demonstrated that one-loop processes in quantum field theory can be expressed in terms of a matrix element whose form is encountered in quantum mechanics, and which can be evaluated using the Heisenberg formalism. We demonstrate how instead this matrix element can be computed using standard results in the path-integral formalism. The technique of operator regularization allows one to extend this approach to arbitrary loop order. No loop-momentum integrals are ever encountered. This technique is illustrated by computing the two-point function in [Formula: see text] theory to one-loop order.

scholarly journals ON THE β-FUNCTION AND CONFORMAL ANOMALY OF NONCOMMUTATIVE QED WITH ADJOINT MATTER FIELDS

2003 ◽  
Vol 18 (15) ◽  
pp. 2591-2607 ◽  
Author(s):  
NÉDA SADOOGHI ◽  
MOJTABA MOHAMMADI
Keyword(s):  
Gauge Theory ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Adjoint Representation ◽  
Conformal Anomaly ◽  
Loop Order ◽  
Path Integral Method ◽  
Β Function ◽  
The One ◽  
Matter Fields

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop β-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using Fujikawa's path integral method. The value of the one-loop β-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom Nf < 3.

scholarly journals GEOMETRICALLY RELATING MOMENTUM CUT-OFF AND DIMENSIONAL REGULARIZATION

2012 ◽  
Vol 10 (02) ◽  
pp. 1250081 ◽  
Author(s):  
SUSAMA AGARWALA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Hopf Algebras ◽  
Dimensional Regularization ◽  
Mass Scale ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coupling Constant ◽  
Regularization Scheme ◽  
Β Function

The β function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the β functions of momentum cut-off regularization and dimensional regularization on scalar field theories by a gauge transformation using the Hopf algebras of the Feynman diagrams of the theories.

ON THE INTERPOLATING SOLUTIONS OF STRING IN DIFFERENT BACKGROUNDS

1992 ◽  
Vol 07 (15) ◽  
pp. 1361-1366 ◽  
Author(s):  
SUDIPTA MUKHERJI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Central Charge ◽  
Space Time ◽  
Time Dependent ◽  
Target Space ◽  
Conformal Field ◽  
Β Function ◽  
Time Dependent Solution

We analyze the β-function equations for string theory in the case when the target space has one space-like (or time-like) direction and the rest is some conformal field theory (CFT) with appropriate central charge and has one nearly marginal operator. We show there always exists a space-(time) dependent solution which interpolates between the original background and the background where CFT is replaced by a new conformal field theory, obtained by perturbing CPT by the nearly marginal operator.

scholarly journals All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method

2016 ◽  
Vol 30 (03) ◽  
pp. 1550259 ◽  
Author(s):  
Paulo R. S. Carvalho
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Critical Exponents ◽  
Lorentz Violation ◽  
Mathematical Explanation ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Loop Order ◽  
Scalar Field Theory ◽  
Loop Level

We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating (LV) O(N) self-interacting [Formula: see text] scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading loop order and later in a proof by induction up to any loop level, the respective [Formula: see text]-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.

scholarly journals Optical theorem and indefinite metric in λϕ4 delta-theory

2020 ◽  
Vol 35 (33) ◽  
pp. 2050214
Author(s):  
Ricardo Avila ◽  
Carlos M. Reyes
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Coupling Parameter ◽  
Effective Field ◽  
Optical Theorem ◽  
Indefinite Metric ◽  
Quantum Field ◽  
Scalar Model ◽  
Loop Order ◽  
Interaction Term

A class of effective field theory called delta-theory, which improves ultraviolet divergences in quantum field theory, is considered. We focus on a scalar model with a quartic self-interaction term and construct the delta theory by applying the so-called delta prescription. We quantize the theory using field variables that diagonalize the Lagrangian, which include a standard scalar field and a ghost or negative norm state. As well known, the indefinite metric may lead to the loss of unitary of the [Formula: see text]-matrix. We study the optical theorem and check the validity of the cutting equations for three processes at one-loop order, and found suppressed violations of unitarity in the delta coupling parameter of the order of [Formula: see text].

scholarly journals Analytic computing methods for precision calculations in quantum field theory

2018 ◽  
Vol 33 (17) ◽  
pp. 1830015 ◽  
Author(s):  
Johannes Blümlein ◽  
Carsten Schneider
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Computing Methods ◽  
Current Status ◽  
Quantum Field ◽  
Loop Order ◽  
Single Scale ◽  
Double Mass ◽  
Mathematical Computation ◽  
And Function

An overview is presented on the current status of main mathematical computation methods for the multiloop corrections to single-scale observables in quantum field theory and the associated mathematical number and function spaces and algebras. At present, massless single-scale quantities can be calculated analytically in QCD to 4-loop order and single mass and double mass quantities to 3-loop order, while zero-scale quantities have been calculated to 5-loop order. The precision requirements of the planned measurements, particularly at the FCC-ee, form important challenges to theory, and will need important extensions of the presently known methods.

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