An Alternative Approach to Canonical Quantization for Introducing Quantum Field Theory: The Double-Slit Experiment Re-Examined

2014 ◽  
pp. 445-452
Author(s):  
Eugenio Bertozzi ◽  
Olivia Levrini
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Canonical Quantization ◽  
Quantum Field ◽  
Alternative Approach ◽  
Double Slit Experiment ◽  
Slit Experiment ◽  
Double Slit

scholarly journals A self-consistency check for unitary propagation of Hawking quanta

2017 ◽  
Vol 32 (33) ◽  
pp. 1750198 ◽  
Author(s):  
Daniel Baker ◽  
Darsh Kodwani ◽  
Ue-Li Pen ◽  
I-Sheng Yang
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Negative Answer ◽  
Space Time ◽  
Quantum Field ◽  
Consistency Check ◽  
Curved Space ◽  
Self Consistency ◽  
Double Slit

The black hole information paradox presumes that quantum field theory in curved space–time can provide unitary propagation from a near-horizon mode to an asymptotic Hawking quantum. Instead of invoking conjectural quantum-gravity effects to modify such an assumption, we propose a self-consistency check. We establish an analogy to Feynman’s analysis of a double-slit experiment. Feynman showed that unitary propagation of the interfering particles, namely ignoring the entanglement with the double-slit, becomes an arbitrarily reliable assumption when the screen upon which the interference pattern is projected is infinitely far away. We argue for an analogous self-consistency check for quantum field theory in curved space–time. We apply it to the propagation of Hawking quanta and test whether ignoring the entanglement with the geometry also becomes arbitrarily reliable in the limit of a large black hole. We present curious results to suggest a negative answer, and we discuss how this loss of naive unitarity in QFT might be related to a solution of the paradox based on the soft-hair-memory effect.

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 A Tiny, Counterintuitive Change to the Mathematics of the Schrodinger Wave Packet and Quantum ElectroDynamics Could Vastly Simplify How We View Nature

2020 ◽  
Vol 17 ◽  
pp. 169-203
Author(s):  
Jeffrey Boyd
Keyword(s):  
Wave Packet ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Zero Energy ◽  
Elementary Wave ◽  
Wave Particle Duality ◽  
The World ◽  
Double Slit Experiment ◽  
Slit Experiment ◽  
Double Slit

This article proposes that an unexpected approach to the mathematics of a Schro ̋dinger wave packet and Quantum Electro-Dynamics (QED), could vastly simplify how we perceive the world around us. It could get rid of most if not all quantum weirdness. Schro ̋dinger’s cat would be gone. Even things that we thought were unquestionably true about the quantum world would change. For example, the double slit experiment would no longer support wave particle duality. Experiments that appeared to say that entangled particles can communicate instantaneously over great distances, would no longer say that. Although the tiny mathematical change is counterintuitive, Occam’s razor dictates that we consider it because it simplifies how we view Nature in such a pervasive way. The change in question is to view a Schro ̋dinger wave packet as part of a larger Elementary Wave traveling in the opposite direction. It is known in quantum mechanics that the same wave can travel in two countervailing directions simultaneously. Equivalent changes would be made to QED and Quantum Field Theory. It is known in QM that there are zero energy waves: for example, the Schro ̋dinger wave carries amplitudes but not energy.

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.

Functional integrals

2021 ◽  
pp. 117-146
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Functional Integral ◽  
Quantum Field ◽  
Functional Integrals ◽  
Generating Functional ◽  
Curved Space ◽  
Functional Representation ◽  
Alternative Approach ◽  
The Subject

This chapter presents an alternative approach to the quantization of fields, an approach that will be critically important for the development of quantum field theory in curved space, which is the subject of the second part of the book. It starts by providing a description of a functional integral in quantum mechanics, concentrating on the representation of an evolution operator. It then considers the functional representation of the Green functions and the generating functional in quantum field theory, including for fermionic theories. After that, perturbative calculations of the generating functionals and their general properties are formulated. The chapter ends with a brief description of ζ‎-regularization as a technique for defining functional determinants.

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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