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The effective action in the renormalizable quantum theory of gravity provides entropy because the total Hamiltonian vanishes. Since it is a renormalization group invariant that is constant in the process of cosmic evolution, we can show conservation of entropy, which is an ansatz in the standard cosmology. Here, we study renormalizable quantum gravity that exhibits conformal dominance at high energy beyond the Planck scale. The current entropy of the universe is derived by calculating the effective action under the scenario of quantum gravity inflation caused by its dynamics. We then argue that ghost modes must be unphysical but are necessary for the Hamiltonian to vanish and for entropy to exist in gravitational systems.

The effective action in the renormalizable quantum theory of gravity provides entropy because the total Hamiltonian vanishes. Since it is a renormalization group invariant that is constant in the process of cosmic evolution, we can show conservation of entropy, which is an ansatz in the standard cosmology. Here, we study renormalizable quantum gravity that exhibits conformal dominance at high energy beyond the Planck scale. The current entropy of the universe is derived by calculating the effective action under the scenario of quantum gravity inflation caused by its dynamics. We then argue that ghost modes must be unphysical but are necessary for the Hamiltonian to vanish and for entropy to exist in gravitational systems. [ABSTRACT FROM AUTHOR]

We prove through path integral Monte Carlo that the covariant Euclidean scalar field theory, φ n r , where r denotes the power of the interaction term and n = s + 1 with s as the spatial dimension and 1 adds imaginary time, such that r = 1 2 , n = 3 can be acceptably quantized using scaled affine quantization (AQ) and the resulting theory is nontrivial, unlike what happens using canonical quantization which finds it trivial. [ABSTRACT FROM AUTHOR]

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD-generating functional integral. We expand the perturbative boundary conditions to both perturbative and nonperturbative fields integrated into the QCD-generating functional integral. It allows us to nullify the CP odd term in the QCD Lagrangian and, thus, to solve the strong CP problem. The presently popular solution to the strong CP problem of introducing axions violates the principle of renormalizability of the Quantum Field Theory, which is very successful phenomenologically. Our solution obeys the principle of renormalizability of the Quantum Field Theory and does not involve new exotic particles like axions. [ABSTRACT FROM AUTHOR]

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD-generating functional integral. We expand the perturbative boundary conditions to both perturbative and nonperturbative fields integrated into the QCD-generating functional integral. It allows us to nullify the CP odd term in the QCD Lagrangian and, thus, to solve the strong CP problem. The presently popular solution to the strong CP problem of introducing axions violates the principle of renormalizability of the Quantum Field Theory, which is very successful phenomenologically. Our solution obeys the principle of renormalizability of the Quantum Field Theory and does not involve new exotic particles like axions.

We suggest a new explanation of the flatness of galaxies rotation curves without invoking dark matter. For this purpose, a new gravitational tensor field is introduced in addition to the metric tensor. [ABSTRACT FROM AUTHOR]

We analyze the R + R² model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a selfconsistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters. [ABSTRACT FROM AUTHOR]

We suggest a new explanation of the flatness of galaxies rotation curves without invoking dark matter. For this purpose, a new gravitational tensor field is introduced in addition to the metric tensor.

In this paper I detail three major mathematical developments that led to the emergence of Yang–Mills theories as the foundation for the standard model of particle physics. In less than 10 years, work on renormalizability, the renormalization group, and lattice quantum field theory highlighted the utility of Yang–Mills type models of quantum field theory by connecting poorly understood candidate dynamical models to emerging experimental results. I use this historical case study to provide lessons for theory construction in physics, and touch on issues related to renormalization group realism from a more historical perspective. In particular, I highlight the fact that much of the hard work in theory construction comes when trying to understand the consequences and representational capacities of a theoretical framework. [ABSTRACT FROM AUTHOR]

We analyze the R+R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV formalism, we derive a classical master equation homogeneous with respect to the antibracket by introducing antifield partners to the background fields and parameters. The constructed model can be renormalized by the standard method of introducing counterterms. This model does not have (exact) multiplicative renormalizability but it does have this property in the physical sector (quasimultiplicative renormalizability). [ABSTRACT FROM AUTHOR]

The stochastic quantization scheme proposed by Parisi and Wu in 1981 is known to have differences from conventional quantum field theory (CQFT) in higher orders. It has been suggested that some of these new features might give rise to a mechanism to explain tiny fermion masses as arising due to radiative corrections. Some features of U(1) axial vector gauge theory in Parisi Wu stochastic quantization are reported. These features are not absent if the theory is formulated in the conventional way. In particular we present arguments for renormalizability of the massive axial vector gauge theory coupled to a massless fermion. [ABSTRACT FROM AUTHOR]

We consider R + R 2 relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, we demonstrate that the R + R 2 model is also unitary contrary to the statements made in the literature, in particular in the work by Stelle. New expressions for the R + R 2 Lagrangian within dimensional regularization and the graviton propagator are derived. We demonstrate that the R + R 2 model is a good candidate for the fundamental quantum theory of gravity.

According to Steven Weinberg, it is the goal of elementary particle physics to search for the final laws of physics, i.e. a simple set of principles from which everything we know about physics can be derived. The main criterion that guides the search for such a set of principles is, according to the author, the sense of inevitability of physical theories, which Weinberg conflates with the idea of beauty. The theoretical physicists' task is, in this sense, to look for constraining principles, such as symmetries and renormalizability, that increase the sense of inevitability of physical laws. It is the goal of this paper to discuss Weinberg's arguments in favor of reductionism, as well as his conception of final theory and the associated concept of "inevitability". [ABSTRACT FROM AUTHOR]

We derive the equation that relates gravity to quantum mechanics: R|mass-shell=8πGc4LSM, where R is the scalar curvature, G is the gravitational constant, c is the speed of light and LSM is the Standard Model Lagrangian, or its future replacement. Implications of this equation are discussed in the paper. In particular, we show (in the last section) that this equation is the transformation that relates four-dimensional physics to two-dimensional physics.

In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz- and CPT-violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz-violating sector can be renormalized by 19 independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize and is not radiatively generated. One-loop computations are also presented and compared with the existing literature. [ABSTRACT FROM AUTHOR]

One of the puzzling aspects of N-dimensional Einstein Gravity (NDEG) augmented by curvature-squared terms is why renormalizability and unitarity, two of the most important properties of any physical theory, cannot be reconciled in its framework. Actually, the reason why these properties are mutually incompatible within the context of generic higher-derivative models, not necessarily related to gravity, is one of the unsolved mysteries of physics. Here, a simple solution to the NDEG riddle, based on the analysis of the interparticle gravitational potential, is presented. The main argument used to support our discussion is that tree-level unitarity and the existence of a singularity in the potential are intertwined. [ABSTRACT FROM AUTHOR]

We study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem of renormalizability of point-like particles. [ABSTRACT FROM AUTHOR]

Effective field theory (EFT) of massive Yang-Mills fields interacting with fermions is considered. Perturbative renormalizability in the framework of EFT is shown. It is argued that the limit of vanishing vector boson mass leads to massless gauge EFT. Possible relevance for the solution to the strong CP problem is discussed. [ABSTRACT FROM AUTHOR]

The superstring and heterotic string effective actions are studied to determine the feasibility of truncating the expansion in powers of α′. The renormalizability properties of the dimensionally reduced actions are then examined. The solutions to the corrected field equations are then shown to satisfy physical conditions on the internal symmetry spaces. [ABSTRACT FROM AUTHOR]

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT-invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particularly needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed. [ABSTRACT FROM AUTHOR]

We construct the most general gauge fixing and the associated Faddeev–Popov ghost term for the SU(2) Yang–Mills theory, which leaves the global U(1) gauge symmetry intact (i.e. the most general Maximal Abelian gauge). We show that the most general form involves eleven independent gauge parameters. Then we require various symmetries which help to reduce the number of independent parameters for obtaining the simpler form. In the simplest case, the off-diagonal part of the gauge fixing term obtained in this way is identical to the modified maximal Abelian gauge term with two gauge parameters which was proposed in the previous paper from the viewpoint of renormalizability. In this case, moreover, we calculate the beta function, anomalous dimensions of all fields and renormalization group functions of all gauge parameters in perturbation theory to one-loop order. We also discuss the implication of these results to obtain information on low-energy physics of QCD. [ABSTRACT FROM AUTHOR]

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized à la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i) the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere SN2. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M4 × S2, the scalars being interpreted as gauge fields on S2. Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n1) × SU(n2) × U(1). Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to reveal new aspects of the theory.

We consider R + R 2 relativistic quantum gravity with the action where all possible terms quadratic in the curvature tensor are added to the Einstein-Hilbert term. This model was shown to be renormalizable in the work by K.S. Stelle. In this paper, we demonstrate that the R + R 2 model is also unitary contrary to the statements made in the literature, in particular in the work by Stelle. New expressions for the R + R 2 Lagrangian within dimensional regularization and the graviton propagator are derived. We demonstrate that the R + R 2 model is a good candidate for the fundamental quantum theory of gravity. [ABSTRACT FROM AUTHOR]

We derive the equation that relates gravity to quantum mechanics: R | m a s s - s h e l l = 8 π G c 4 L S M , where R is the scalar curvature, G is the gravitational constant, c is the speed of light and L S M is the Standard Model Lagrangian, or its future replacement. Implications of this equation are discussed in the paper. In particular, we show (in the last section) that this equation is the transformation that relates four-dimensional physics to two-dimensional physics. [ABSTRACT FROM AUTHOR]