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.

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.

Quantum Field Theory

2020 ◽  
pp. 237-288
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Canonical Quantization ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coordinate Space ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Transfer Matrix Formalism

Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.

scholarly journals NONCOMMUTATIVE QUANTIZATION FOR NONCOMMUTATIVE FIELD THEORY

2007 ◽  
Vol 22 (06) ◽  
pp. 1181-1200 ◽  
Author(s):  
YASUMI ABE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Correlation Functions ◽  
Canonical Quantization ◽  
Noncommutative Space ◽  
Quantization Scheme ◽  
Quantum Field ◽  
Noncommutative Field Theory ◽  
Commutative Field ◽  
Noncommutative Parameter

We present a new procedure for quantizing field theory models on a noncommutative space–time. Our new quantization scheme depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by this quantization yields exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after the quantization. This implies, for instance, that the noncommutativity may be incorporated in the process of quantization, rather than in the action as conventionally done.

scholarly journals PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250136 ◽  
Author(s):  
MIGUEL-ANGEL SANCHIS-LOZANO ◽  
J. FERNANDO BARBERO G. ◽  
JOSÉ NAVARRO-SALAS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fock Space ◽  
Dimensional Space ◽  
Canonical Quantization ◽  
Prime Numbers ◽  
Large Integer ◽  
Quantum Field ◽  
Dimensional Space Time ◽  
Prime Fields

Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space–time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators [Formula: see text] — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.

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.

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