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Employing the little group symmetry within the spinor-helicity formalism to constrain scattering amplitudes

Parmar, Samyak LU (2021) FYTK02 20211
Theoretical Particle Physics
Abstract
This thesis aims to describe the little group scaling and how it simplifies the calculation of scattering amplitudes. The little group has the defining property that it leaves a particular four-momentum invariant, which is used to describe how the internal structure of a particle is transformed under the little group. An important part in the study of little group scaling is the spinor-helicity formalism, which is based on spinors of helicity h = ±1/2. This formalism comes with some interesting identities which already simplify the calculation of amplitudes. Finally, we show that applying little group scaling to massless particles with complex momenta in the spinor-helicity formalism fully constrains their (mathematical) three-particle... (More)
This thesis aims to describe the little group scaling and how it simplifies the calculation of scattering amplitudes. The little group has the defining property that it leaves a particular four-momentum invariant, which is used to describe how the internal structure of a particle is transformed under the little group. An important part in the study of little group scaling is the spinor-helicity formalism, which is based on spinors of helicity h = ±1/2. This formalism comes with some interesting identities which already simplify the calculation of amplitudes. Finally, we show that applying little group scaling to massless particles with complex momenta in the spinor-helicity formalism fully constrains their (mathematical) three-particle amplitudes. (Less)
Popular Abstract
The framework that we use to study the fundamental building blocks of the universe is called quantum field theory. An important idea here is that there exists a ‘field’ of each of the fundamental particles throughout 'spacetime'. The study of the fundamental particles that make up the universe is a complicated subject. In physics, we often exploit symmetries to simplify such complicated subjects. In this thesis, the centerpiece is one such symmetry encapsulated by the so called 'little group', discovered by Eugene Wigner in 1939. The little group introduces an element of symmetry of the particles with respect to spacetime itself.

When we talk about spacetime, we must consider Einstein's special theory of relativity. It essentially gives... (More)
The framework that we use to study the fundamental building blocks of the universe is called quantum field theory. An important idea here is that there exists a ‘field’ of each of the fundamental particles throughout 'spacetime'. The study of the fundamental particles that make up the universe is a complicated subject. In physics, we often exploit symmetries to simplify such complicated subjects. In this thesis, the centerpiece is one such symmetry encapsulated by the so called 'little group', discovered by Eugene Wigner in 1939. The little group introduces an element of symmetry of the particles with respect to spacetime itself.

When we talk about spacetime, we must consider Einstein's special theory of relativity. It essentially gives an account of how spacetime changes from the perspective of different observers moving at different velocities. If we consider particles purely in this framework, we do not consider their internal structure. However, particles also possess an internal structure. The little group gives an insight into this internal structure and how it transforms when observed from the perspective of different observers.

Quantum field theory is probabilistic, meaning that we find probabilities for events occurring, rather than a definite answer. The calculation of these probabilities is often not an easy task. This is where we use the little group symmetry to simplify the calculations. Thus, we use the insight into the internal structure of the particles to simplify the calculation of probabilities describing the occurrence of events involving these particles. (Less)
Please use this url to cite or link to this publication:
author
Parmar, Samyak LU
supervisor
organization
course
FYTK02 20211
year
type
M2 - Bachelor Degree
subject
keywords
little group scaling, little group, spinor-helicity formalism
report number
LU-TP 21-18
language
English
id
9056716
date added to LUP
2021-06-24 09:12:05
date last changed
2021-06-24 09:12:05
@misc{9056716,
  abstract     = {{This thesis aims to describe the little group scaling and how it simplifies the calculation of scattering amplitudes. The little group has the defining property that it leaves a particular four-momentum invariant, which is used to describe how the internal structure of a particle is transformed under the little group. An important part in the study of little group scaling is the spinor-helicity formalism, which is based on spinors of helicity h = ±1/2. This formalism comes with some interesting identities which already simplify the calculation of amplitudes. Finally, we show that applying little group scaling to massless particles with complex momenta in the spinor-helicity formalism fully constrains their (mathematical) three-particle amplitudes.}},
  author       = {{Parmar, Samyak}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Employing the little group symmetry within the spinor-helicity formalism to constrain scattering amplitudes}},
  year         = {{2021}},
}