8 research outputs found
Second-Order Fermions
It has been proposed several times in the past that one can obtain an
equivalent, but in many aspects simpler description of fermions by first
reformulating their first-order (Dirac) Lagrangian in terms of two-component
spinors, and then integrating out the spinors of one chirality ( primed
or dotted). The resulting new Lagrangian is second-order in derivatives, and
contains two-component spinors of only one chirality. The new second-order
formulation simplifies the fermion Feynman rules of the theory considerably,
the propagator becomes a multiple of an identity matrix in the field
space. The aim of this thesis is to work out the details of this formulation
for theories such as Quantum Electrodynamics, and the Standard Model of
elementary particles. After having developed the tools necessary to establish
the second-order formalism as an equivalent approach to spinor field theories,
we proceed with some important consistency checks that the new formulation is
required to pass, namely the presence or absence of anomalies in their
perturbative and non-perturbative description, and the unitarity of the
S-Matrix derived from their Lagrangian. Another aspect which is studied is
unification, where we seek novel gauge-groups that can be used to embed all of
the Standard Model content: forces and fermionic representations. Finally, we
will explore the possibility to unify gravity and the Standard Model when the
former is seen as a diffeomorphism invariant gauge-theory.Comment: Ph.D. Thesis, 281p
Second-order fermions
It has been proposed several times in the past that one can obtain an equivalent, but in many aspects simpler description of fermions by first reformulating their first-order (Dirac) Lagrangian in terms of two-component spinors, and then integrating out the spinors of one chirality (e.g.primed or dotted). The resulting new Lagrangian is second-order in derivatives, and contains two-component spinors of only one chirality. The new second-order formulation simplifies the fermion Feynman rules of the theory considerably, e.g. the propagator becomes a multiple of an identity matrix in the field space. The aim of this thesis is to work out the details of this formulation for theories such as Quantum Electrodynamics, and the Standard Model of elementary particles. After having developed the tools necessary to establish the second-order formalism as an equivalent approach to spinor field theories, we proceed with some important consistency checks that the new formulation is required to pass, namely the presence or absence of anomalies in their perturbative and non-perturbative description, and the unitarity of the S-Matrix derived from their Lagrangian. Another aspect which is studied is unification, where we seek novel gauge-groups that can be used to embed all of the Standard Model content: forces and fermionic representations. Finally, we will explore the possibility to unify gravity and the Standard Model when the former is seen as a diffeomorphism invariant gauge-theory
Second-order fermions
It has been proposed several times in the past that one can obtain an equivalent, but in many aspects simpler description of fermions by first reformulating their first-order (Dirac) Lagrangian in terms of two-component spinors, and then integrating out the spinors of one chirality (e.g.primed or dotted). The resulting new Lagrangian is second-order in derivatives, and contains two-component spinors of only one chirality. The new second-order formulation simplifies the fermion Feynman rules of the theory considerably, e.g. the propagator becomes a multiple of an identity matrix in the field space. The aim of this thesis is to work out the details of this formulation for theories such as Quantum Electrodynamics, and the Standard Model of elementary particles. After having developed the tools necessary to establish the second-order formalism as an equivalent approach to spinor field theories, we proceed with some important consistency checks that the new formulation is required to pass, namely the presence or absence of anomalies in their perturbative and non-perturbative description, and the unitarity of the S-Matrix derived from their Lagrangian. Another aspect which is studied is unification, where we seek novel gauge-groups that can be used to embed all of the Standard Model content: forces and fermionic representations. Finally, we will explore the possibility to unify gravity and the Standard Model when the former is seen as a diffeomorphism invariant gauge-theory
OPE Convergence in Conformal Field Theory
We clarify questions related to the convergence of the OPE and conformal
block decomposition in unitary Conformal Field Theories (for any number of
spacetime dimensions). In particular, we explain why these expansions are
convergent in a finite region. We also show that the convergence is
exponentially fast, in the sense that the operators of dimension above Delta
contribute to correlation functions at most exp(-a Delta). Here the constant
a>0 depends on the positions of operator insertions and we compute it
explicitly.Comment: 26 pages, 6 figures; v2: a clarifying note and two refs added; v3:
note added concerning an extra constant factor in the main error estimate,
misprint correcte
Second order Standard Model
It is known, though not commonly, that one can describe fermions using a second order in derivatives Lagrangian instead of the first order Dirac one. In this description the propagator is scalar, and the complexity is shifted to the vertex, which contains a derivative operator. In this paper we rewrite the Lagrangian of the fermionic sector of the Standard Model in such second order form. The new Lagrangian is extremely compact, and is obtained from the usual first order Lagrangian by integrating out all primed (or dotted) 2-component spinors. It thus contains just half of the 2-component spinors that appear in the usual Lagrangian, which suggests a new perspective on unification. We sketch a natural in this framework SU(2)×SU(4)⊂SO(9) unified theory