Schwarzschild-like Wormholes in Asymptotically Safe Gravity

In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor Xμν as a source to improved field equations, and promotes the Newton’s constant into a running coupling constant. In particular, we check whether the radial energy conditions are satisfied and compare with the results obtained from the usual theory. We show that only in the particular case of the wormhole being asymptotically flat(Schwarzschild Wormholes) that the radial energy conditions are satisfied at the throat, depending on the chosen values for its radius r0. In contrast, in the general Schwarzschild-like case, there is no possibility of the energy conditions being satisfied nearby the throat, as in the usual case. After that, we calculate the radial state parameter, ω(r), in r0, in order to verify what type of cosmologic matter is allowed at the wormhole throat, and we show that in both cases there is the possibility of the presence of exotic matter, phantom or quintessence-like matter. Finally, we give the ω(r) solutions for all regions of space. Interestingly, we find that Schwarzschild-like Wormholes with excess of solid angle of the sphere in the asymptotic limit have the possibility of having non-exotic matter as source for certain values of the radial coordinate r. Furthermore, it was observed that quantum gravity corrections due the ASG necessarily imply regions with phantom-like matter, both for Schwarzschild and for Schwarzschild-like wormholes. This reinforces the supposition that a phantom fluid is always present for wormholes in this context.

Perturbative Versus Non-Perturbative Quantum Field Theory: Tao’s Method, the Casimir Effect, and Interacting Wightman Theories

We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a well-defined (rigorous) mathematical sense, as well as some of the few existent mathematically precise results on fully quantized field theories. Emphasis is brought on how the mathematical contributions help to elucidate or illuminate certain conceptual aspects of the theory when applied to real physical phenomena, in particular, the singular nature of quantum fields. In a first part, we present a comprehensive review of divergent versus asymptotic series, with qed as background example, as well as a method due to Terence Tao which conveys mathematical sense to divergent series. In a second part, we apply Tao’s method to the Casimir effect in its simplest form, consisting of perfectly conducting parallel plates, arguing that the usual theory, which makes use of the Euler-MacLaurin formula, still contains a residual infinity, which is eliminated in our approach. In the third part, we revisit the general theory of nonperturbative quantum fields, in the form of newly proposed (with Christian Jaekel) Wightman axioms for interacting field theories, with applications to “dressed” electrons in a theory with massless particles (such as qed), as well as unstable particles. Various problems (mostly open) are finally discussed in connection with concrete models.

Parabolic eigenvarieties via overconvergent cohomology

Let $$\mathcal {G}$$ G be a connected reductive group over $$\mathbf {Q}$$ Q such that $$G = \mathcal {G}/\mathbf {Q}_p$$ G = G / Q p is quasi-split, and let $$Q \subset G$$ Q ⊂ G be a parabolic subgroup. We introduce parahoric overconvergent cohomology groups with respect to Q, and prove a classicality theorem showing that the small slope parts of these groups coincide with those of classical cohomology. This allows the use of overconvergent cohomology at parahoric, rather than Iwahoric, level, and provides flexible lifting theorems that appear to be particularly well-adapted to arithmetic applications. When Q is a Borel, we recover the usual theory of overconvergent cohomology, and our classicality theorem gives a stronger slope bound than in the existing literature. We use our theory to construct Q-parabolic eigenvarieties, which parametrise p-adic families of systems of Hecke eigenvalues that are finite slope at Q, but that allow infinite slope away from Q.

Yang-Mills Equations of General Connections and a Certain Solutions in the Quaternionic Hopf Fibration Over Four-Sphere

We investigate a version of Yang-Mills theory by means of general connections. In order to deduce a basic equation, which we regard as a version of Yang-Mills equation, we construct a self-action density using the curvature of general connections. The most different point from the usual theory is that the solutions are given in pairs of two general connections. This enables us to get nontrivial solutions as general connections. Especially, in the quaternionic Hopf fibration over four-sphere, we demonstrate that there certainly exist nontrivial solutions, which are made by twisting the well-known BPST anti-instanton.

Categories: Between Cubes and Globes. Sketch I

For a finite partially ordered set I, we define an abstract polytope PI which is a cube or a globe in the cases of discrete or linear poset, respectively. For a poset P, we have built a small category ♦P with finite lower subsets in P as objects. This category ♦P = ♦P+♦P- is factorized into a product of two wide subcategories ♦P+ of faces and ♦P- of degenerations. One can imagine a degeneration from I to J ⊂ I as a projection of an abstract polytope PI to the subspace spanned by J. Morphisms in ♦P+ with fixed target I are identified with faces of PI . The composition in ♦P admits the natural geometric interpretation. On the category ♦I of presheaves on ♦I , we construct a monad of free category in two steps: for a terminal presheaf, the free category is obtained via a generalized nerve construction; in the general case, the cells of a nerve are colored by elements of the initial presheaf. Strict P-fold categories are defined as algebras over this monad. All constructions are functorial in P. The usual theory of globular and cubical higher categories can be translated in a natural way into our general context.

Cyclically Deformed Defects and Topological Mass Constraints

A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite localized energy of cyclically generated defects. The idea of obtaining cyclically deformed defects concerns the possibility of regenerating a primitive (departing) defect structure through successive, unidirectional, and eventually irreversible, deformation processes. Our technique is applied on kink-like and lump-like solutions in models described by a single real scalar field such that extensions to quantum mechanics follow the usual theory of deformed defects. The preliminary results show that the cyclic device supports simultaneously kink-like and lump-like defects into 3- and 4-cyclic deformation chains with topological mass values closed by trigonometric and hyperbolic deformations. In a straightforward generalization, results concerning the analytical calculation ofN-cyclic deformations are obtained, and lessons regarding extensions from more elaborated primitive defects are depicted.

Minimum dissipative relaxed states applied to laboratory and space plasmas

The usual theory of plasma relaxation, based on the selective decay of magnetic energy over the (global) magnetic helicity, predicts a force-free state for a plasma. Such a force-free state is inadequate to describe most realistic plasma systems occurring in laboratory and space plasmas as it produces a zero pressure gradient and cannot couple magnetic fields with flow. A different theory of relaxation has been proposed by many authors, based on a well-known principle of irreversible thermodynamics, the principle of minimum entropy production rate which is equivalent to the minimum dissipation rate of energy. We demonstrate the applicability of minimum dissipative relaxed states to various self-organized systems of magnetically confined plasma in the laboratory and in the astrophysical context. Such relaxed states are shown to produce a number of basic characteristics of laboratory plasma confinement systems and solar arcade structure.

Infinite Computation in the Equivalent Transformation Model

There are many logic programs that do not terminate but perform useful computation in some sense. The usual theory of logic programming adopts least fixpoints to define the meaning of programs, which fails to capture the intended meaning of infinite computation. To give an appropriate sense to useful infinite computation, the theory of logic programming has adopted greatest fixpoints in place of least fixpoints. However, this solution developed in logic paradigm can not explain finite and infinite computation in a unified manner. This paper proposes a new approach to infinite computation based on the equivalent transformation paradigm, where infinite computation is regarded as repeated equivalent transformations and is given appropriate sense in the same way as the usual finite computation.

Energy bounds for some non-standard problems in thermoelasticity

A.E. Green F.R.S. and P.M. Naghdi developed two theories of thermoelasticity, called type II and type III, which are likely to be more natural candidates for the identification of a thermoelastic body than the usual theory. We here derive energy bounds for a class of problem in which the ‘initial data’ are given as a combination of data at time t =0 and at a later time t = T . Such problems are in vogue in the mathematical literature and may be used, for example, to give estimates of solution behaviour in an improperly posed problem where one wishes to continue a solution backward in time.

SYMMETRY BREAKING IN GAUGE FIELD THEORY DUE TO NONCOMMUTATIVE SPACETIME

It is well known that a typical Yang–Mills Gauge Field is mediated by massless Bosons. It is only through a symmetry breaking mechanism, as in the Salam–Weinberg model that the quanta of such an interaction field acquire a mass in the usual theory. Here, we demonstrate that without taking recourse to the usual symmetry breaking mechanism, it is still possible to achieve this, given a noncommutative geometrical underpinning for spacetime.