Mass Gap and Violation of Discrete Symmetries in Quantum Field Theory

1966 ◽  
Vol 152 (4) ◽  
pp. 1505-1507
Author(s):  
F. Strocchi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Discrete Symmetries ◽  
Quantum Field ◽  
Mass Gap

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.

scholarly journals ABOUT NEUTRAL KAONS AND SIMILAR SYSTEMS: FROM QUANTUM FIELD THEORY TO EFFECTIVE MASS MATRICES

2005 ◽  
Vol 20 (01) ◽  
pp. 41-75
Author(s):  
B. MACHET
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Mass ◽  
Discrete Symmetries ◽  
Binary Systems ◽  
Mass Matrix ◽  
Orthogonal Basis ◽  
Quantum Field ◽  
Cpt Symmetry ◽  
Mass Matrices

Systems of neutral interacting mesons are investigated, concerning in particular their description by an effective Hamiltonian, with a special emphasis on discrete symmetries. Several ambiguities are pointed out. First, the connection to quantum field theory, in which the physical masses [Formula: see text] and [Formula: see text] are the poles of the full renormalized propagator, shows that, for mass-split binary systems, two mass matrices rather than a single effective one are at work; they correspond to the two values [Formula: see text] and [Formula: see text] of the momentum squared. Transformation properties of the physical eigenstates by discrete symmetries may not reflect the ones of these two mass matrices (and those of the Lagrangian at any given p2). Then, after showing that a bi-orthogonal basis has to be used to diagonalize the complex mass matrix of such unstable systems, and not a bi-unitary transformation, we turn to the ambiguity linked to the commutation of the fields of the K0 and of its charge conjugate [Formula: see text]: any constant effective mass matrix is defined, in the [Formula: see text] basis, up to arbitrary diagonal antisymmetric terms; I use this freedom to deform it in various ways, in both the [Formula: see text] and (KL,KS) basis, and I study the consequences on the spectrum. CPT symmetry is specially concerned. An effective mass matrix can always be cast into a CPT invariant form, and only T violating eigenstates can never be cast into CP eigenstates. The dual formalism of |in> and <out| states and bi-orthogonal basis, suitable for nonnormal matrices, is used. In a subsequent work, the fundamental roles played by the normality of the mass matrix and CPT symmetry in the framework of quantum field theory will be investigated in connection with experimental results.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field
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