Search results for " formulation"

Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice

2005

We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity whic…

Quantized Fields and Their Interpretation

2013

This chapter deals with the quantum theory of systems with an infinite number of degrees of freedom and provides elements of quantum field theory.

Special Section on Fractional Operators in the Analysis of Mechanical Systems Under Stochastic Agencies

2017

GENERALIZED GAUGE TRANSFORMATIONS AND HIDDEN SYMMETRY IN THE STANDARD MODEL

1992

A recently proposed, new construction of the Standard Model based on the graded Lie algebra SU (2|1) is analyzed in some depth. The essential ingredient is an algebraic superconnection which incorporates both the gauge fields and the Higgs fields and whose curvature automatically leads to a spontaneously broken realization of the theory. The mechanism of hiding the original algebraic structure is unorthodox and is due to the specific, "noncommutative" realization of SU (2|1). The model is characterized by a constant background supercurvature which is invariant under arbitrary, constant SU (2|1) gauge transformations. This background field whose effect is analogous to the action of a consta…

Measure dependence of 2D simplicial quantum gravity

1995

We study pure 2D Euclidean quantum gravity with $R^2$ interaction on spherical lattices, employing Regge's formulation. We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by using a finite-size scaling Ansatz in the expectation value of $R^2$. To check on effects of the path integral measure we investigate two scale invariant measures, the "computer" measure $dl/l$ and the Misner measure $dl/\sqrt A$.

Covariant phase space quantization of the Jackiw-Teitelboim model of two-dimensional gravity

1992

Abstract On the basis of the covariant phase space formulation of field theory we analyze the Jackiw-Teitelboim model of two-dimensional gravity on a cylinder. We compute explicitly the symplectic structure showing that the (reduced) phase space is the cotangent bundle of the space of conjugacy classes of the PSL(2, R ) group. This makes it possible to quantize the theory exactly. The Hilbert space is given by the character functions of the PSL (2, R ) group. As a byproduct, this implies the complete equivalence with the PSL (2, R )-topological gravity model.

Tri/Bi-maximal lepton mixing and leptogenesis

2009

In models with flavour symmetries added to the gauge group of the Standard Model the CP-violating asymmetry necessary for leptogenesis may be related with low-energy parameters. A particular case of interest is when the flavour symmetry produces exact Tri-Bimaximal lepton mixing leading to a vanishing CP-violating asymmetry. In this paper we present a model-independent discussion that confirms this always occurs for unflavoured leptogenesis in type I see-saw scenarios, noting however that Tri-Bimaximal mixing does not imply a vanishing asymmetry in general scenarios where there is interplay between type I and other see-saws. We also consider a specific model where the exact Tri-Bimaximal mi…

A theory for scotogenic dark matter stabilised by residual gauge symmetry

2020

Dark matter stability can result from a residual matter-parity symmetry, following naturally from the spontaneous breaking of the gauge symmetry. Here we explore this idea in the context of the $\mathrm{SU(3)_c \otimes SU(3)_L \otimes U(1)_X \otimes U(1)_{N}}$ electroweak extension of the standard model. The key feature of our new scotogenic dark matter theory is the use of a triplet scalar boson with anti-symmetric Yukawa couplings. This naturally implies that one of the light neutrinos is massless and, as a result, there is a lower bound for the $\rm 0\nu\beta\beta$ decay rate.

CP violation in decays of the lightest supersymmetric particle with bilinearly broken R parity

2002

Supersymmetric models with broken R-parity induced by lepton number violating terms provide a calculable framework for neutrino masses and mixings. Within models with bilinear R-parity breaking six new physical phases appear which are potential sources of novel CP-violating phenomena compared to the minimal supersymmetric extension of the standard model. We consider CP-violating observables in the decays of the lightest supersymmetric particle in this class of models. We show that: (i) Neutrino physics requires a strong correlation between three different pairs of phases, thus reducing the effective number of new phases to three. (ii) CP-violating phenomena in decays of the lightest supersy…

Minimal 3-loop neutrino mass models and charged lepton flavor violation

2020

We study charged lepton flavor violation for the three most popular 3-loop Majorana neutrino mass models. We call these models "minimal" since their particle content correspond to the minimal sets for which genuine 3-loop models can be constructed. In all the three minimal models the neutrino mass matrix is proportional to some powers of Standard Model lepton masses, providing additional suppression factors on top of the expected loop suppression. To correctly explain neutrino masses, therefore large Yukawa couplings are needed in these models. We calculate charged lepton flavor violating observables and find that the three minimal models survive the current constraints only in very narrow …