Twistor diagrams and massless Møller scattering

1983 ◽  
Vol 385 (1788) ◽  
pp. 207-228 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Electrodynamics ◽  
General Type ◽  
Infrared Divergence ◽  
Scattering Data ◽  
Quantum Field ◽  
First Order ◽  
Moller Scattering ◽  
Correct Account ◽  
Massless Fields

The theory of twistor diagrams, as devised by Penrose, is intended to lead to a manifestly finite account of scattering amplitudes in quantum field theory. The theory is here extended to a more general type of interaction between massless fields than has hitherto been described. It is applied to the example of first-order massless Møller scattering in quantum electrodynamics. It is shown that earlier studies of this example have failed to render a correct account, in particular by overlooking an infrared divergence, but that the scattering data can nevertheless be represented within the twistor formalism.

A twistor approach to the regularization of divergences

1985 ◽  
Vol 397 (1813) ◽  
pp. 341-374 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Infrared Divergence ◽  
Standard Theory ◽  
Quantum Field ◽  
New Formalism ◽  
First Order ◽  
Finite Theory ◽  
Finite Quantity ◽  
Modified Theory

One object of the twistor programme, as developed principally by R. Penrose, is the production of a manifestly finite theory of scattering in quantum field theory. Earlier work has shown that progress towards this goal is obstructed even at the first-order level, by the appearance of an infrared divergence in the standard theory. New studies in many-dimensional contour integration now suggest a simple but very powerful modification to this branch of twistor theory, in which the full (as opposed to the projective) twistor space plays an essential role. In this modified theory there arise natural contour-integral expressions with the effect of eliminating the infrared divergence previously noted, and replacing it by a finite quantity. This regularization can be specified by using a formalism of ‘inhomogeneous twistor diagrams’. The interpretation of this new formalism is not yet wholly clear, but the inhomogeneity can be seen as a means of relinquishing the concept of space-time point, while preserving light-cone structure. It therefore suggests a quite fresh approach to the divergences of quantum field theory.

Understanding Phase Transitions in Supersymmetric Quantum Electrodynamics With Resurgence Theory

2021 ◽  
Vol 1 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
Series Expansion ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Perturbative Series

Using resurgence theory to describe phase transitions in quantum field theory shows that information on non-perturbative effects like phase transitions can be obtained from a perturbative series expansion.

CONSISTENT CHIRAL QUANTUM ELECTRODYNAMICS

1991 ◽  
Vol 06 (14) ◽  
pp. 1299-1304 ◽  
Author(s):  
G. DEMARCO ◽  
C. FOSCO ◽  
R.C. TRINCHERO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Quantum Field ◽  
Massless Fermions

We construct a unitary and renormalizable quantum field theory in 3+1 dimensions describing the interaction of chiral massless fermions with massive or massless photons.

scholarly journals Logarithmic expansion of field theories: higher orders and resummations

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Vincenzo Branchina ◽  
Alberto Chiavetta ◽  
Filippo Contino
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Order ◽  
Weak Coupling ◽  
Field Theories ◽  
Quantum Field ◽  
First Order ◽  
Free Theory ◽  
Formal Expansion ◽  
The Way

AbstractA formal expansion for the Green’s functions of a quantum field theory in a parameter $$\delta $$ δ that encodes the “distance” between the interacting and the corresponding free theory was introduced in the late 1980s (and recently reconsidered in connection with non-hermitian theories), and the first order in $$\delta $$ δ was calculated. In this paper we study the $${\mathcal {O}}(\delta ^2)$$ O ( δ 2 ) systematically, and also push the analysis to higher orders. We find that at each finite order in $$\delta $$ δ the theory is non-interacting: sensible physical results are obtained only resorting to resummations. We then perform the resummation of UV leading and subleading diagrams, getting the $${\mathcal {O}}(g)$$ O ( g ) and $${\mathcal {O}}(g^2)$$ O ( g 2 ) weak-coupling results. In this manner we establish a bridge between the two expansions, provide a powerful and unique test of the logarithmic expansion, and pave the way for further studies.

scholarly journals Convergence in Quantum Field Theory without Use of Renormalization

2019 ◽  
Author(s):  
Biswaranjan Dikshit
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Electrodynamics ◽  
Ad Hoc ◽  
Probability Amplitude ◽  
Quantum Field ◽  
Counter Term ◽  
Self Energy ◽  
Calculated Probability ◽  
Conventional Methods

In quantum field theory (QFT), it is well known that when Feynman diagrams containing loops are evaluated to account for self interactions, probability amplitude comes out to be infinite which is physically not admissible. So, to make the QFT convergent, various renormalization methods are conventionally followed in which an additional (infinite) counter term is postulated which neutralizes the original infinity generated by diagram. The resulting finite values of amplitudes have agreed with experiments with surprising accuracy. However, proponents of renormalization methods acknowledged that this ad-hoc procedure of subtraction of infinity from infinity to reach at a finite value is not at all satisfactory and there is no physical basis for bringing in the counter term. So, it is desirable to establish a method in QFT which does not generate any infinite term (thus not requiring renormalization), but which predicts same results as conventional methods do. In this paper, we describe such a technique taking self interaction quantum electrodynamics diagram representing electron or photon self energy. In our method, no problem of infinity arises and hence renormalization is not necessary. Still, the dependence of calculated probability amplitude on physical variables in our technique comes out to be same as conventional methods. Using similar procedure, we hope, the problem of non-renormalizability of quantum gravity may be solved in future.

scholarly journals A novel view on successive quantizations, leading to increasingly more “miraculous” states

2019 ◽  
Vol 34 (23) ◽  
pp. 1950186 ◽  
Author(s):  
Matej Pavšič
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Wave Packet ◽  
Time Derivative ◽  
Point Particle ◽  
Order Equation ◽  
Quantum Field ◽  
First Order ◽  
Complex Wave

A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

scholarly journals Quantum Ostrogradsky theorem

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Hayato Motohashi ◽  
Teruaki Suyama
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
First Order ◽  
Higher Derivative ◽  
Original Theorem ◽  
Classical Lagrangian

Abstract The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such non-degenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

scholarly journals Non-Equilibrium Quantum Electrodynamics in Open Systems as a Realizable Representation of Quantum Field Theory of the Brain

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 43 ◽  
Author(s):  
Akihiro Nishiyama ◽  
Shigenori Tanaka ◽  
Jack A. Tuszynski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Time Evolution ◽  
Central Region ◽  
Quantum Electrodynamics ◽  
Quantum Tunneling ◽  
Evolution Equations ◽  
Open Systems ◽  
Quantum Field ◽  
The Brain

We derive time evolution equations, namely the Klein–Gordon equations for coherent fields and the Kadanoff–Baym equations in quantum electrodynamics (QED) for open systems (with a central region and two reservoirs) as a practical model of quantum field theory of the brain. Next, we introduce a kinetic entropy current and show the H-theorem in the Hartree–Fock approximation with the leading-order (LO) tunneling variable expansion in the 1st order approximation for the gradient expansion. Finally, we find the total conserved energy and the potential energy for time evolution equations in a spatially homogeneous system. We derive the Josephson current due to quantum tunneling between neighbouring regions by starting with the two-particle irreducible effective action technique. As an example of potential applications, we can analyze microtubules coupled to a water battery surrounded by a biochemical energy supply. Our approach can be also applied to the information transfer between two coherent regions via microtubules or that in networks (the central region and the N res reservoirs) with the presence of quantum tunneling.

scholarly journals The principle of stationary variance in quantum field theory

2014 ◽  
Vol 29 (05) ◽  
pp. 1450026 ◽  
Author(s):  
Fabio Siringo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum System ◽  
Quantum Electrodynamics ◽  
Best Approximation ◽  
Variational Approach ◽  
Heisenberg Model ◽  
Gauge Theories ◽  
Quantum Field

The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.

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