Spectral-function sum rules in Lagrangian field theory: An application of the renormalization group

1976 ◽  
Vol 13 (4) ◽  
pp. 961-967 ◽  
Author(s):  
William I. Weisberger
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Spectral Function ◽  
Sum Rules ◽  
Lagrangian Field Theory

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals On the notion of gauge symmetries of generic Lagrangian field theory

2009 ◽  
Vol 50 (1) ◽  
pp. 012903 ◽  
Author(s):  
G. Giachetta ◽  
L. Mangiarotti ◽  
G. Sardanashvily
Keyword(s):  
Field Theory ◽  
Gauge Symmetries ◽  
Lagrangian Field Theory

Asymptotic SU(5) symmetry and spectral-function sum rules

1979 ◽  
Vol 5 (7) ◽  
pp. 885-891 ◽  
Author(s):  
V P Gautam ◽  
B Bagchi
Keyword(s):  
Spectral Function ◽  
Sum Rules

STOCHASTIC FIELD THEORY AND RENORMALIZATION GROUP APPROACH TO CRITICAL BEHAVIORS IN THERMO FIELD DYNAMICS

1989 ◽  
Vol 04 (09) ◽  
pp. 2185-2210
Author(s):  
B. BHATTACHARYA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Finite Temperature ◽  
Internal Field ◽  
Point Of View ◽  
Internal Space ◽  
Theoretic Approach ◽  
Stochastic Field ◽  
Stochastic Fields ◽  
Renormalization Group Approach

We have studied here the critical behaviors in a simple model from the point of view of the renormalization group at finite temperature utilizing the Stochastic field theoretic approach towards a finite temperature field theory. To this end, thermofield dynamics has been formulated in terms of Stochastic fields in the external and internal space and the thermal average of the two-point correlation function of the internal field functions is related with the order parameter. The thermodynamical functions and the critical phenomena are then studied constructing the generating functionals involving Stochastic fields.

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

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