Two-Point Function Reduction of Four-Point Amputated Functions and Transformations in FF and RA Basis in a Real-Time Finite Temperature NJL Model

Based on a general analysis of Green functions in the real-time thermal field theory, we have proven that the four-point amputated functions in an NJL model in the fermion bubble diagram approximation behave like usual two-point functions. We expound the thermal transformations of the matrix propagators for a scalar bound state in the FF basis and in the RA basis respectively. The resulting physical causal, advanced and retarded propagators are respectively identical to corresponding ones derived in the imaginary-time formalism, and this shows once again the complete equivalence of the two formalisms of thermal field theory on the discussed problem in the NJL model.     

Quantum information theory

A conceptual analysis of the classical information theory of Shannon (1948) shows that this theory cannot be directly generalized to the usual quantum case. The reason is that in the usual quantum mechanics of closed systems there is no general concept of joint and conditional probability. Using, however, the generalized quantum mechanics of open systems (A. Kossakowski 1972) and the generalized concept of observable (“semiobservable”, E.B. Davies and J.T. Lewis 1970) it is possible to construct a quantum information theory being then a straightforward generalization of Shannon's theory.     

Purely quadrupolar spin-1 Ising model in a transverse field

A quantum Ising-like spin-1 model characterized by quadrupolar interaction, coupled to an external anisotropic field with both dipole and quadrupole momenta is analyzed. The general phase diagram (including temperature), as well as order parameter, specific heat, and susceptibility are evaluated in the mean-field approximation and exibit a rich structure with transitions of 2° and 1° order and tricritical points. ForT=0 the phase diagram is examined also by a recently formulated improved version of mean-field theory which has the usual mean-field theory as its zero-th order approximation.     

Toward a unification of “everything” with gravity

Combining the ideas of gauge interactions with a global supersymmetry, we build a unified model in six dimensions step by step, starting with a single generation of leptons and ending with three generations of leptons and colored quarks forming a supermultiplet characterized by a most general extensionN=8. The puzzle of supersymmetric partners, such as the gravitino, photino, s-leptons, and s-quarks, is seen in a new light. The supersymmetry is only a global one, whereas local supersymmetry and supergravity are replaced by the theory of gauge interactions and by the usual general relativity of Einstein.     

Quantum measurement theory including initial correlations and observables with continuous spectra

In the framework of the quantum mechanical measurement theory we study measurements where the state of the object and the state of the apparatus are initially already correlated. We show that the usual difficulties extend to the measuring schemes considered here. The general structure of the theory is clarified.     

Die Abweichung vom Exponentialzerfall angeregter Zustände

In the theory of line breadth phenomena excited amplitudes must not exactly follow the usual exponential decay law. This fact is well known from fundamental mathematical considerations, although there is not any unique form for the corresponding deviation. In this paper we seek a new expression for the decay, based upon a rather general field model of mass zero. The result is a good approximation for times ≈ 1/γ and yields the exact asymptotic solution. A modification to a model with mass ≠0 does not in general lead to other formulations of the solution.     

The gauge in general relativity. II

The present paper and a companion work are intended as one possible realization of a non-customary gauge theory of general relativity-as set forth in only broad outline in an earlier work. In this first paper, it is found that both radar echo delay and the perihelion shift differ slightly from their customary expressions. Unfortunately, it is also found that the usual statement of the principle of equivalence does not hold in the present formulation. Finally, in the second paper, a single cosmological model is investigated that appears to be promising.This work forms part of a Ph.D. dissertation by L.S.     

The Brans-Dicke scalar field in Einstein-Cartan theory

In the framework of Einstein-Cartan (EC) theory, the Brans-Dicke (BD) theory is considered and it is found that a scalar field nonminimally coupled to the gravitational field gives rise to torsion, even though the scalar field has zero spin. The metric equations stay the same if the coupling constant is rescaled, but the equations of motion of a test particle, derived from the conservation equations, differ from those of the usual BD theory without torsion. The gravitational red-shift value differs considerably from the usual prediction of general theory of relativity (GTR), and rules out the possibility of a torsion version of BD theory for<6.     

Uniqueness theorems in ideal magnetofluid dynamics

Summary If based on the hyperbolic PDE general theory, the proof of a uniqueness theorem for the ideal magnetofluid-dynamic evolution problem presupposes a number of laborious verifications, as well as a good acquaintance with that theory. This paper provides a direct, ?ad hoc? alternative proof, which is immediately accessible to the nonspecialist and also removes a significant, but unnecessary, limitation tied to the usual theory.     

Primordial perturbations and non-gaussianities in Ho?ava-Lifshitz gravity

We investigate primordial perturbations and non-gaussianities in the Ho?ava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Ho?ava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are " slow-roll suppressed” in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on Ho?ava-Lifshitz gravity.     

On the expansion of a quantum field theory around a topological sector

The idea of treating quantum general relativistic theories in a perturbative expansion around a topological theory has recently received attention, in the quantum gravity literature. We investigate the viability of this idea by applying it to conventional Yang–Mills theory on flat spacetime. This theory admits indeed a formulation as a modified topological theory, like general relativity. We find that the expansion around the topological theory coincides with the usual expansion around the free abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. On the other hand, we point out that the relation of this expansion with the actual quantum BF theory is far from being transparent. Some implications for gravity are discussed.     

Cohomological Yang–Mills theories on Kähler 3-folds

We study topological gauge theories with N_c=(2,0) supersymmetry based on stable bundles on general Kähler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual holomorphic bundle by including a holomorphic 3-form. The correlation functions of the model describe complex 3-dimensional generalizations of Donaldson–Witten type invariants. We show that the path integral can be written as a sum of contributions from stable bundles and a complex 3-dimensional version of Seiberg–Witten monopoles. We study certain deformations of the theory, which allow us to consider the situation of reducible connections. We shortly discuss situations of reduced holonomy. After dimensional reduction to a Kähler 2-fold, the theory reduces to Vafa–Witten theory. On a Calabi–Yau 3-fold, the supersymmetry is enhanced to N_c=(2,2). This model may be used to describe classical limits of certain compactifications of (matrix) string theory.     

A new approach to the theory of relativity. II. The general theory of relativity

The considerations of Part I are extended and the experimental data and hypotheses that led to the establishment of the general theory of relativity are analyzed. It is found that one of the fundamental assumptions is that light is propagated homogeneously; i.e., by using arbitrary systems of coordinates, propagation of light can be represented by a homogeneous quadratic form. This is shown to be an assumption that can be verified by experiment, at least in principle. As a result of adding a number of further assumptions to this, the usual formalism of the general theory of relativity can be established. In the above point of view, the general theory of relativity—like any other theory—cannot be built upad hoc, but is built on distinct physical hypotheses, each of which can be subjected to test by experiment.     

A Discussion on Finite Quasi-cardinals in Quasi-set Theory

Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardinal definition fail for collections of indistinguishable objects. In a recent work, Domenech and Holik have proposed a definition of quasi-cardinality in Q. They claimed their definition of quasi-cardinal not only avoids the introduction of that notion as a primitive one, but also that it may be seen as a first step in the search for a version of Q that allows for a greater representative power. According to them, some physical systems can not be represented in the usual formulations of the theory, when the quasi-cardinal is considered as primitive. In this paper, we discuss their proposal and aims, and also, it is presented a modification from their definition we believe is simpler and more general.     

TRANSVERSE TRANSPORT PROCESSES OF CHARGED PARTICLE SYSTEMS IN A STRONG MAGNETIC FIELD (II) SOME DISCUSS IONS ABOUT THE BOLTZMANN EQUATION

In this article, it is pointed out that in a strong magnetic field the usual Boltzmann Equation with Lorentz force term is inconsistent with the fundamental requirements of the general theory of non-equilibrium statistical mechanics. Furthermore, if a collision term corresponding to particles in different gyroorbits is used, we find that all the transport coefficients are exactly zero.     

Characterization of standard clocks by means of light rays and freely falling particles

A mathematical characterization of standard clocks (i.e., clocks measuring proper time) is presented, which yields an experimental method to test whether or not a given clock is a standard clock. The only tools needed are light rays and freely falling particles. For this reason our method fits very well in the framework of the axiomatic approach to space-time theory given by Ehlers, Pirani, and Schild [1], where just light rays and freely falling particles are used as primitive concepts. As the underlying space-time model we use a Weyl manifold (instead of a Lorentz manifold, which is the usual model of general relativity); this generalization is motivated by [1].     

An equation of motion method for deriving microscopic effective interactions in a correlated model space

Starting from a diagrammatic analysis of the equation of motion method, we derive an effective interaction theory for a correlated model space where the basis vectors correspond physically to the addition of valence particles and/or holes to the true ground state of the core nucleus. The resulting effective interaction $\text{V}$ is valence linked and connected, energy independent, and contains folded diagrams. In addition, it gives directly model eigenvectors with amplitudes that correspond to spectroscopic factors. With terms having the same number of folds grouped together, the general structure of $\text{V}$ is very simple. This is very useful in the application of the present theory to actual microscopic nuclear structure calculations. The treatment of core projection insertions is discussed in some detail. A proof of the cancellation of the disconnected diagrams is given. When folded diagrams are summed up using a partial summation method, the present effective interaction theory is shown to be consistent with the usual Green function theory for many-body problems.     

A Theory of Evolving Natural Constants Based on the Unification of General Theory of Relativity and Dirac's Large Number Hypothesis

Taking Dirac's large number hypothesis as true, we have shown [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703] the inconsistency of applying Einstein's theory of general relativity with fixed gravitation constant G to cosmology, and a modified theory for varying G is found, which reduces to Einstein's theory outside the gravitating body for phenomena of short duration in small distances, thereby agrees with all the crucial tests formerly supporting Einstein's theory. The modified theory, when applied to the usual homogeneous cosmological model, gives rise to a variable cosmological tensor term determined by the derivatives of G, in place of the cosmological constant term usually introduced ad hoc. Without any free parameter the theoretical Hubble's relation obtained from the modified theory seems not in contradiction to observations, as Dr. Wang's preliminary analysis of the recent data indicates [Commun. Theor. Phys. (Beijing, China) 42 (2004) 703]. As a complement to Commun. Theor. Phys. (Beijing, China) 42 (2004) 703 we shall study in this paper the modification of electromagnetism due to Dirac's large number hypothesis in more detail to show that the approximation of geometric optics still leads to null geodesics for the path of light, and that the general relation between the luminosity distance and the proper geometric distance is still valid in our theory as in Einstein's theory, and give the equations for homogeneous cosmological model involving matter plus electromagnetic radiation. Finally we consider the impact of the modification to quantum mechanics and statistical mechanics, and arrive at a systematic theory of evolving natural constants including Planck's ħ as well as Boltzmann's k_B by finding out their cosmologically combined counterparts with factors of appropriate powers of G that may remain truly constant to cosmologically long time.