Dirac and Faddeev–Jackiw quantization of a five-dimensional Stüeckelberg theory with a compact dimension

A detailed Hamiltonian analysis for a five-dimensional Stüeckelberg theory with a compact dimension is performed. First, we develop a pure Dirac’s analysis of the theory; we show that after performing the compactification, the theory is reduced to four-dimensional Stüeckelberg theory plus a tower of Kaluza–Klein modes. We develop a complete analysis of the constraints, we fix the gauge and we show that there are present pseudo-Goldstone bosons. Then we quantize the theory by constructing the Dirac brackets. As complementary work, we perform the Faddeev–Jackiw quantization for the theory under study, and we calculate the generalized Faddeev–Jackiw brackets, we show that both the Faddeev–Jackiw and Dirac’s brackets are the same. Finally we discuss some remarks and prospects.     

Removing the Forbidden States in a 4<Emphasis Type="Italic">α</Emphasis> System

In previous calculations we considered some α systems with local and non-local αα potentials, and we have shown that the nonlocality nature of the cluster–cluster interaction is indispensable. In those calculations we investigated systems in which we had a maximum of three αα pairs, and we succeeded, although it was not so easy, to remove the forbidden states with a satisfactory degree. In this paper we try to apply the same techniques and same potentials in describing ¹⁶O as a 4α system, where now we have a six αα pairs, but unfortunately we find out that it is difficult to remove the forbidden states in this system. We therefore devote this paper to show in some detail the difficulty we face.     

SU(3) LIMIT OF U(6/20) SUPERSYMMETRY IN NUCLEI

In this paper we discuss the SU(3) limit of U(6/20) supersymmetry. First we derive the reduction formulas of the relevant group chain. Then we discuss the dynamical symmetry. Finally we make comparison between the theoretical calculation and experimental measurement in the case of nucleus .²³⁵₉₂U₁₄₃     

Rumsfeld hadrons

A missing link in the Standard Model is understanding hadrons, particles that respond to the strong interactions. In this article I summarise our knowledge in three classes, which are reminiscent of Donald Rumsfeld's (in)famous: ‘things that we know we know; things that we know we don't know; and things that we don't know that we don't know'. Recent discoveries in particle physics concerning strongly interacting hadrons fall into those categories. It is of course the third category that is the most tantalising, but lessons from the first two may help resolve the third.     

Astrogeometry: Toward mathematical foundations

Inimage processing (e.g., inastronomy), the desired black-and-white image is, from the mathematical viewpoint, aset. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse approximation. Hence, it is desirable to find the family that it isthe best in some reasonable sense. In this paper, we show how the problems of choosing the optimal family of sets can be formalized and solved. As a result of the described general methodology, forastronomical images, we get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, we have atheoretical explanation for these shapes.     

Quantum friction in a periodic potential

In this paper we study the quantum friction problem using the Hamiltonian of Caldirola-Kanai for a periodic Mathieu's type potential. In the sequel we study the lattice electron with friction we introduce a new effective Hamiltonian of the Caldirola-Kanai form for a Bloch's band. Finally we study the cases of closed solutions of Schrödinger's equation.     

Alloy-disorder scattering of the interacting electron gas in quantum wells and heterostructures of Al x Ga1 − x As

The question whether alloy disorder is screened or unscreened is of fundamental importance. Therefore, we calculate the mobility of the interacting two-dimensional electron gas as realized in Al _x Ga_{1 ? x} As quantum wells and heterostructures in the presence of alloy-disorder scattering. For the screening we use the randomphase approximation and we include many-body effects due to exchange and correlation. We propose to determine the alloy disorder potential V _AD from mobility measurements. If we use V _AD = 1.04 eV we can explain recent experimental results obtained for quantum wells and heterostructures with ultrahigh mobility. From the anomalous linear temperature dependence of the mobility measured in heterostructures, we conclude that the alloy disorder is screened. More experiments are needed to confirm the screening of the alloy disorder and we propose some measurements.     

Quantization of conformal gravity: Another approach to the renormalization of gravity

The non-renormalizability of quantum gravity poses a great problem to the construction of any unified field theory of all known interactions. Normally, we start with a unitary theory of gravity and investigate its renormalization properties. This is the first of a series of papers where we start with the opposite approach, beginning with a renormalizable theory and investigating its unitarity structure. In particular, we study non-perturbative approaches to the quantization of conformal gravity. Using ADM coordinates, we perform the canonical quantization of the Weyl action C_μναβ², which is renormalizable and is also local scale invariant. Although this theory is certainly not unitary in perturbation theory, we speculate that unitarity may be restored when we approach this theory non-perturbatively, by examining the possibility of different phase transitions.     

(2 + 1)-Dimensional Solutions in F(R) Gravity

Motivated by the well-known charged BTZ black holes, we look for (2 + 1)-dimensional solutions of F(R) gravity. At first we investigate some near horizon solutions and after that we obtain asymptotically Lifshitz black hole solutions. Finally, we discuss about rotating black holes with exponential form of F(R) theory.     

On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree

In the present paper, we study a new kind of p-adic measures for q?+?1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.     

Energy loss of a heavy particle near 3D charged rotating hairy black hole

In this paper, we start with a black brane and construct a specific space-time which violates hyperscaling. To obtain the string solution, we apply the Null-Melvin Twist and KK reduction. Using the difference action method, we study the thermodynamics of the system to obtain a Hawking–Page phase transition. To have hyperscaling violation, we need to consider $\theta =\frac{d}{2}.$ In this case, the free energy $F$ is always negative and our solution is thermal radiation without a black hole. Therefore, we find that there is no Hawking–Page transition. Also, we discuss the stability of the system and all thermodynamical quantities.     

Unraveling supersymmetry at future colliders

After a quick review of the current limits on sparticle masses, we outline the prospects for their discovery at future colliders. We then proceed to discuss how precision measurements of sparticle masses can provide information about how SM superpartners acquire their masses. Finally, we examine how we can proceed to establish whether or not any new physics discovered in the future is supersymmetry, and describe how we might zero in on the framework of SUSY breaking. In this connection, we review sparticle mass measurements at future colliders, and point out that some capabilities of experiments ate ⁺ e ⁻ linear colliders may have been over-stated in the literature.     

Arithmetic properties of mirror map and quantum coupling

We study some arithmetic properties of the mirror maps and the quantum Yukawa couplings for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to characterize the mirror map in each case. For algebraic K3 surfaces, we solve the equation in terms of theJ-function. By deriving explicit modular relations we prove that some K3 mirror maps are algebraic over the genus zero function fieldQ(J). This leads to a uniform proof that those mirror maps have integral Fourier coefficients. Regarding the maps as Riemann mappings, we prove that they are genus zero functions. By virtue of the Conway-Norton conjecture (proved by Borcherds using Frenkel-Lepowsky-Meurman's Moonshine module), we find that these maps are actually the reciprocals of the Thompson series for certain conjugacy classes in the Griess-Fischer group. This also gives, as an immediate consequence, a second proof that those mirror maps are integral. We thus conjecture a surprising connection between K3 mirror maps and the Thompson series. For threefolds, we construct a formal nonlinear ODE for the quantum coupling reduced modp. Under the mirror hypothesis and an integrality assumption, we derive modp congurences for the Fourier coefficients. For the quintics, we deduce, (at least for 5×d) that the degreed instanton numbersn _d are divisible by 5³ — a fact first conjectured by Clemens.Research supported by grant DE-FG02-88-ER-25065     

Demonstration of the Double Q2-Rescaling Model

In this paper we have demonstrated the double Q²-rescaling model (DQ²RM) of parton distribution functions of nucleon bounded in nucleus. For different χ regions in I-A deep inelastic scattering process we take different approaches: in high χ region (0.1 ≤ χ ≤ 0.7)we use the distorted QCD vacuum model which resulted from topologically multi-connected domain vacuum structure of nucleus; in low χ region (10^-4 ≤ χ ≤ 10^-3) we adopt the Glauber (Mueller) multi-scat tering formula for gluon coherently rescat tering in nucleus. From these two approaches we show that the rescaling parton distribution functions in bound nucleon are in good agreement with those we got from DQ²RM, thus the validity for this phenomenological model is demonstrated.     

Algebraic entropy,symmetries and linearization of quad equations consistent on the cube

We discuss the non–autonomous nonlinear partial difference equations belonging to Boll classi?cation of quad graph equations consistent around the cube. We show how starting from the compatible equations on a cell we can construct the lattice equations, its Bäcklund transformations and Lax pairs. By carrying out the algebraic entropy calculations we show that the H⁴ trapezoidal and the H⁶ families are linearizable and in a few examples we show how we can effectively linearize them.     

Long-Time Bath Correlations in the Pollak–Grabert–Hänggi Theory

We analyze some cases for which the Pollak–Grabert–Hänggi theory on the activated rate processes for generalized Langevin dynamics exhibits unexplained disagreements with numerical results. First we analyze carefully the PGH theory and we show that a kind of Markovian hypothesis implicitly made in the reasoning is sometimes violated. Then we propose modifications of the original theory in order to take into account the possible effects caused by this violation, and we compare the corrected results with simulations.     

Electro-optic response of metal halide $$\hbox {CsPbI}_3$$: A first-principles study

In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken ⁴¹Ca with a single neutron in the ⁴⁰Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for ¹⁷O, ⁴¹Ca, ⁴⁹Ca and ⁵⁷Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.     

Thermostatistics of Deformed Bosons and Fermions

Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.     

Hamiltonian Dynamics for Einstein’s Action in <Emphasis Type="Italic">G</Emphasis>→0 Limit

The Hamiltonian analysis for the Einstein’s action in G→0 limit is performed. Considering the original configuration space without involve the usual ADM variables we show that the version G→0 for Einstein’s action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis.     

Massive vector multiplets in supergravity

Starting from a vector multiplet we construct general lagrangians using the tensor calculus. After a Weyl rescaling and other field redefinitions we find lagrangians for the massive spin $\text{(1,}\text{1}\text{2}\text{,}\text{1}\text{2}\text{, 0)}$ model coupled to supergravity. Among the class of lagrangians which we consider we find no supersymmetry breaking.