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.
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.
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.
118739941
Novel symmetries in vector Schwinger model
We derive nilpotent and absolutely anticommuting (anti-)co-BRST symmetry transformations for the bosonized version of (1+1)-dimensional (2D) vector Schwinger model. These symmetry transformations turn out to be the analog of co-exterior derivative of differential geometry as the total gauge-fixing term remains invariant under it. The exterior derivative is realized in terms of the (anti-)BRST symmetry transformations of the theory whereas the bosonic symmetries find their analog in the Laplacian operator. The algebra obeyed by these symmetry transformations turns out to be exactly same as the algebra obeyed by the de Rham cohomological operators of differential geometry.
121188687
Basic canonical brackets in the gauge field theoretic models for the Hodge 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.
118498683
Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries
We discuss consequences of combining the effective $Z_2\times Z_2$ symmetry of the tri-bimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized $Z_2\times Z_2$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to non-zero $\theta_{13}$ and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized $Z_2\times Z_2$ symmetry of the mass matrix can arise from the $A_4$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real parameters and leads to determination of the absolute neutrino mass scale as a function of the reactor angle $\theta_{13}$.
53455412
Negative specific heat in a thermodynamic model of multifragmentation
We consider a soluble model of multifragmentation which is similar in spirit to many models which have been used to fit intermediate energy heavy ion collision data. In this model, ${c}_{v}$ is always positive but for finite nuclei ${c}_{p}$ can be negative for some temperatures and pressures. Furthermore, negative values of ${c}_{p}$ can be obtained in canonical treatment. One does not need to use the microcanonical ensemble. Negative values for ${c}_{p}$ can persist for systems as large as 200 particles but this depends upon parameters used in the model calculation. As expected, negative specific heats are absent in the thermodynamic limit.
121387686
Hybrid Monte Carlo simulations of a two-dimensional gauge theory
Through a study of the dynamics of the two-dimensional U(1) pure gauge theory we find exponential slowing down in barrier penetration problems. We verify that the dynamical critical exponent in HMC can be tuned exactly to 1, and that normal and gauge fixed updates have equal cost.
120031477
Theory of Longitudinal Photons in Quantum Electrodynamics
The radiation field is quantized by introducing four types of photons - two transverse, one longitudinal, and one scalar. The scalar photons are treated by using an indefinite metric, and it is found necessary to modify the usual supplementary condition slightly. The present theory offers a justification for the symmetrical treatment of the four components of the electromagnetic potential, recently applied by a number of authors, and proves to be very convenient in applications. The results of physical interest, however, are the same as obtained from the ordinary formulation.
122963652
Intrinsic density and energy dependence: Exchange effects in alpha-nucleus scattering
The exchange effect for the alpha-nucleus potential has been computed by folding in the density matrices with a finite range effective interaction. The ''effective'' exchange interaction is both density and energy dependent. The potential agrees closely with phenomenology.