118967100
PSEUDO-HERMITIAN INTERACTIONS IN DIRAC THEORY: EXAMPLES
We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both cases we show that the energy spectrum is real and all the other features of nonrelativistic pseudo-Hermitian formulation are present. Using the spectral method, the positive definite metric operator (η) has been calculated explicitly for both the models to ensure positive definite norms for the state vectors.
118643338
An Interacting Gauge Field Theoretic Model for the Hodge Theory: Basic Canonical Brackets
We derive the basic canonical brackets amongst the creation and annihilation operators for a two (1 + 1)-dimensional (2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field (A_\mu) is coupled with the fermionic Dirac fields (\psi and \bar \psi). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries (and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta (corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries (and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.
121188687
Basic canonical brackets in the gauge field theoretic models for the Hodge theory
118402302
Superfield approach to nilpotent symmetries in 3D Jackiw-Pi model of massive non-Abelian theory
In the available literature, only the Becchi-Rouet-Stora-Tyutin (BRST) symmetries are known for the Jackiw-Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent (s_{(a)b}^2 = 0) and absolutely anticommuting (s_b \,s_{ab} + s_{ab}\, s_b = 0) (anti-)BRST transformations s_{(a)b} corresponding to the usual Yang-Mills gauge transformations of this model by exploiting the "augmented" superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang-Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci-Ferrari restriction which plays a key role in the proof of absolute anticommutativity of s_{(a)b}. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field \rho from our superfield formalism which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and/or absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.
118646248
Predictions from High Scale Mixing Unification Hypothesis
We investigate the renormalization group evolution of masses and mixing angles of Majorana neutrinos under the ``high scale mixing unification'' hypothesis. Assuming the unification of quark-lepton mixing angles at a high scale, we show that all the experimentally observed neutrino oscillation parameters can be obtained, within the $3\text{\ensuremath{-}}\ensuremath{\sigma}$ range, through the running of corresponding renormalization group equations provided neutrinos have the same charge parity and are quasidegenerate. One of the novel results of our analysis is that ${\ensuremath{\theta}}_{23}$ turns out to be nonmaximal and lies in the second octant. Furthermore, we derive new constraints on the allowed parameter space for the unification scale, supersymmetry breaking scale and $\mathrm{tan}\ensuremath{\beta}$, for which the high scale mixing unification hypothesis works.
118367187
A NOTE ON THE (ANTI-)BRST INVARIANT LAGRANGIAN DENSITIES FOR THE FREE ABELIAN 2-FORM GAUGE THEORY
We show that the previously known off-shell nilpotent and absolutely anticommuting (sb sab + sab sb = 0) Becchi–Rouet–Stora–Tyutin (BRST) transformations (sb) and anti-BRST transformations (sab) are the symmetry transformations of the appropriate Lagrangian densities of a four (3+1)-dimensional (4D) free Abelian 2-form gauge theory which do not explicitly incorporate a very specific constrained field condition through a Lagrange multiplier 4D vector field. The above condition, which is the analogue of the Curci–Ferrari restriction of the non-Abelian 1-form gauge theory, emerges from the Euler–Lagrange equations of motion of our present theory and ensures the absolute anticommutativity of the transformations s(a)b. Thus, the coupled Lagrangian densities, proposed in our present investigation, are aesthetically more appealing and more economical.
120893061
Models of the proton spin structure
A phenomenological model of spin sharing by the constituents of a proton is constructed, based on the recent EMC measurement of the spin dependent structure function and knowledge of the unpolarized parton densities.
118621901
Radiative and seesaw threshold corrections to the S3 symmetric neutrino mass matrix
Abstract We systematically analyze the radiative corrections to the S 3 symmetric neutrino mass matrix at high energy scale, say the GUT scale, in the charged lepton basis. There are significant corrections to the neutrino parameters both in the Standard Model (SM) and Minimal Supersymmetric Standard Model (MSSM) with large tan ⁡ β , when the renormalization group evolution (RGE) and seesaw threshold effects are taken into consideration. We find that in the SM all three mixing angles and atmospheric mass squared difference are simultaneously obtained in their current 3 σ ranges at the electroweak scale. However, the solar mass squared difference is found to be larger than its allowed 3 σ range at the low scale in this case. There are significant contributions to neutrino masses and mixing angles in the MSSM with large tan ⁡ β from the RGEs even in the absence of seesaw threshold corrections. However, we find that the mass squared differences and the mixing angles are simultaneously obtained in their current 3 σ ranges at low energy when the seesaw threshold effects are also taken into account in the MSSM with large tan ⁡ β .
123149979
Ghost-field formalism for vector particles
118396346
Isoscaling, symmetry energy and thermodynamic models
Abstract The isoscaling parameter usually denoted by α depends upon both the symmetry energy coefficient and the isotopic contents of the dissociating systems. We compute α in theoretical models: first in a simple mean field model and then in thermodynamic models using both grand canonical and canonical ensembles. For finite systems the canonical ensemble is much more appropriate. The model values of α are compared with a much used standard formula. Next we turn to cases where in experiments, there are significant deviations from isoscaling. We show that in such cases, although the grand canonical model fails, the canonical model is capable of explaining the data.
123705690
Stringy restrictions on the Scherk-Schwarz mechanism
The authors consider the sigma model describing the propagation of a bosonic string in a manifold of the type M4(X)K obtained by compactification of D=26 spacetime using the Scherk-Schwarz mechanism. The requirement of 2D conformal invariance (at the 1-loop level) of this sigma model is shown to impose rather stringent restrictions on the mass parameters used in the Scherk-Schwarz mechanism. Implications for the background field mass spectrum in the model considered by Scherk and Schwarz (1979) are examined.