Approximate determination of the mass gap in quantum field theory using the method of finite elements

1986 ◽  
Vol 34 (10) ◽  
pp. 3149-3155 ◽  
Author(s):  
Carl M. Bender ◽  
Kimball A. Milton
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Elements ◽  
Approximate Determination ◽  
Quantum Field ◽  
Method Of Finite Elements ◽  
Mass Gap

On the Mathematical Structure of the New-Tamm-Dancoff Procedure

1981 ◽  
Vol 36 (5) ◽  
pp. 421-428
Author(s):  
W. Feist
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Mathematical Structure ◽  
Approximate Determination ◽  
Quantum Field ◽  
C Algebras ◽  
Canonical Anticommutation Relations ◽  
Functional Algebra ◽  
Joint Treatment

Abstract The New Tamm-Dancoff method is a procedure for the approximate determination of differences of eigenvalues in quantum field theory. This procedure can be formulated mathematically in the framework of the theory of C*-algebras, especially in our case by using von Neumann's infinite tensor products. Calculational rules are presented for operators which obey the canonical anticommutation relations. The concept of the CAR tensor product is introduced for the joint treatment of a system algebra and the associated functional algebra, A conjugation is discussed which will be needed for a proof of equivalence in II.

Renormalization Group: From a general concept to numbers

2019 ◽  
pp. 69-80
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
General Concept ◽  
Quantum Field ◽  
Fixed Dimension ◽  
Perturbative Renormalization ◽  
Borel Transformation

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.

A NEW LOOK AT GOLDSTONE’S THEOREM

1992 ◽  
Vol 04 (spec01) ◽  
pp. 49-83 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
SERGIO DOPLICHER ◽  
ROBERTO LONGO ◽  
JOHN E. ROBERTS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Broken Symmetries ◽  
Mass Gap ◽  
Algebraic Setting ◽  
Local Quantum ◽  
Physical Mass ◽  
Continuous Symmetries ◽  
Conserved Currents

The appearance of spontaneously broken symmetries and its bearing on the physical mass spectrum are analyzed in the algebraic setting of local quantum field theory. Within this setting, a generalization of Goldstone’s Theorem is established which does not rely on the existence of conserved currents. Continuous symmetries not satisfying the premises of the theorem can be spontaneously broken even in the presence of a mass gap.

Zeta-function regularization of quantum field theory

1990 ◽  
Vol 68 (7-8) ◽  
pp. 620-629 ◽  
Author(s):  
A. Y. Shiekh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Zeta Function ◽  
Analytic Continuation ◽  
Quantum Field ◽  
Four Dimensions ◽  
Group Functions

Analytic continuation leads to the finite renormalization of a quantum field theory. This is illustrated in a determination of the two loop renormalization group functions for [Formula: see text] in four dimensions.

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