scholarly journals Z0 →2γ AND THE TWISTED COPRODUCT OF THE POINCARÉ GROUP

2007 ◽  
Vol 22 (32) ◽  
pp. 6133-6146 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
S. G. JO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Result ◽  
Invariant Theory ◽  
Massive Particle ◽  
Lepton Number ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group ◽  
Special Case

Yang's theorem forbids the process Z0 →2γ in any Poincaré invariant theory if photons are bosons and their two-particle states transform under the Poincaré group in the standard way (under the standard coproduct of the Poincaré group). This is an important result as it does not depend on the assumptions of quantum field theory. Recent work on noncommutative geometry requires deforming the above coproduct by the Drinfel'd twist. We prove that Z0 →2γ is forbidden for the twisted coproduct as well. This result is also independent of the assumptions of quantum field theory. As an illustration of the use of our general formulae, we further show that Z0 →ν+ ν is forbidden for the standard or twisted coproduct of the Poincaré group if the neutrino is massless, even if lepton number is violated. This is a special case of our general result that a massive particle of spin j cannot decay into two identical massless particles of the same helicity if j is odd, regardless of the coproduct used.

scholarly journals Supersymmetry: Early Roots That Did Not Grow

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Cecilia Jarlskog
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Poincaré Group ◽  
Poincare Group

This paper is about early roots of supersymmetry, as found in the literature from 1940s and early 1950s. There were models where the power of “partners” in alleviating divergences in quantum field theory was recognized. However, other currently known remarkable features of supersymmetry, such as its role in the extension of the Poincaré group, were not known. There were, of course, no supersymmetric nonabelian quantum field theories in those days.

scholarly journals Different Quantum Field Constructions in the (1/2,0) ⊕ (0,1/2) Representation

1997 ◽  
Vol 12 (36) ◽  
pp. 2741-2748 ◽  
Author(s):  
Valeri V. Dvoeglazov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Neutrino Physics ◽  
Present Situation ◽  
Quantum Field ◽  
Concrete Realization ◽  
Intrinsic Parity ◽  
Special Case

We present another concrete realization of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner. Considering the special case of the (1/2,0)⊕ (0,1/2) field and developing the Majorana–McLennan–Case–Ahluwalia construction for neutrino, we show that fermion and its antifermion can have the same intrinsic parity. The construction can be applied to explain the present situation in neutrino physics.

ON THE COMPUTATION OF THE TURAEV-VIRO MODULE OF A KNOT

1998 ◽  
Vol 07 (07) ◽  
pp. 843-856 ◽  
Author(s):  
H. ABCHIR ◽  
C. BLANCHET
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fundamental Domain ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Abelian Cover ◽  
Topological Quantum ◽  
Special Case

Let M be the manifold obtained by 0-framed surgery along a knot K in the 3-sphere. A Topological Quantum Field Theory assigns to a fundamental domain of the universal abelian cover of M an operator, whose non-nilpotent part is the Turaev-Viro module of K. In this paper, using surgery formulas, we give a matrix presentation for the Turaev-Viro module of any knot K, in the case of the (Vp, Zp) TQFT of Blanchet, Habegger, Masbaum and Vogel. We do the computation for a family of knots in the special case p = 8, and note the relation with the fibering question.

COMBINATORIC MASSEY–MILNOR LINKING THEORY

2011 ◽  
Vol 20 (06) ◽  
pp. 927-938 ◽  
Author(s):  
CHUN-CHUNG HSIEH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Configuration Space ◽  
Invariant Theory ◽  
Knot Theory ◽  
Quantum Field ◽  
Perturbative Quantum ◽  
Knot Diagrams ◽  
Chern Simons ◽  
Milnor Invariant

In this paper following the scheme of Massey–Milnor invariant theory [C. C. Hsieh, Combinatoric and diagrammatic studies in knot theory J. Knot Theory Ramifications16 (2007) 1235–1253; C. C. Hsieh, Massey-Milnor linking = Chern-Simons-Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903; C. C. Hsieh and S. W. Yang, Chern-Simons-Witten configuration space integrals in knot theory, J. Knot Theory Ramifications14 (2005) 689–711], we studied the first non-vanishing linkings of knot theory in ℝ3 and also derived the combinatorial formulae from which we could read out the invariants directly from the knot diagrams. Though the theme is calculus, the idea comes from perturbative quantum field theory.

Words and formulas in quantum field theory: Disentangling $262#and reassembling the basic concepts for teaching

2013 ◽  
Vol 26 (3) ◽  
pp. 372-380
Author(s):  
Eugenio Bertozzi ◽  
Elisa Ercolessi ◽  
Olivia Levrini
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Canonical Quantization ◽  
Quantum Field ◽  
Alternative Teaching ◽  
Multilevel Structure ◽  
Pros And Cons ◽  
University Level ◽  
The University ◽  
Special Case

We address some problem related to teaching quantum field theory at the university level. After a discussion of the pros and cons of the canonical quantization approach, we present an alternative teaching proposal. The novelty of this approach rests on the idea of using a multilevel structure, where the levels of phenomenology, formalism and interpretation are related but distinguishable. In this context, the quantization of the electromagnetic field, which is taken as a paradigmatic case in the standard approach, is addressed as a special case and studied only in the last step.

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