Related papers: Universal Einstein-Hermitian Metrics

We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic…

We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…

This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.

We systematically study Lorentz symmetry extensions in quantum field theories (QFTs) and their 't Hooft anomalies via cobordism. The total symmetry $G'$ can be expressed in terms of the extension of Lorentz symmetry $G_L$ by an internal…

Applying Clausius relation, $\delta Q=TdS$, to apparent horizon of a FRW universe with any spatial curvature, and assuming that the apparent horizon has temperature $T=1/(2\pi \tilde {r}_A)$, and a quantum corrected entropy-area relation,…

Gauss's Lemma is revised by showing that the point set association of the double tangential space with the tangential space of a Riemannian manifold is not the identity. The latter point set association is called a metrical distortion, an…

Because of two $3\sigma$ anomalies, the Standard Model (SM) fit of the precision electroweak data has a poor confidence level, $CL= 0.02$. Since both anomalies involve challenging systematic issues, it might appear that the SM could still…

We characterize uniform $k$-rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call $\iota$-numbers. The characterization follows from an abstract statement…

We investigate four-fermion interactions with $N$-component fermion in Einstein universe for arbitrary space-time dimensions ($2 \leq D<4$). It is found that the effective potential for composite operator $\overline{\psi}\psi$ is calculable…

This work sets out to compute the corrections to the Euler-Heisenberg effective action that arise from spacetime-dependent background anisotropies that violate Lorentz symmetry. To accomplish our task, we evaluate the functional determinant…

We show that at long lengthscales and low energies and to leading order in 1/N expansion, the anisotropic QED in 2+1 dimensions renormalizes to an isotropic limit. Consequently, the (Euclidean) relativistic invariance of the theory is…

The Busemann-Petty problem asks whether origin-symmetric convex bodies in real Euclidean n-space with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative for n less or equal to 4 and negative if n…

The Golomb-Welch conjecture states that there are no perfect $e$-error-correcting Lee codes in $\mathbb{Z}^n$ ($PL(n,e)$-codes) whenever $n\geq 3$ and $e\geq 2$. A special case of this conjecture is when $e=2$. In a recent paper of A.…

Paper withdrawn, due a crucial error in the proof of Lemma 4.3: thus Theorems 1.2 and 1.3 remain unproven.

The complete set of one-loop anomalous dimensions for general Effective Field Theories (EFTs) is derived using on-shell methods. Combined with previous findings for the bosonic sector, the obtained results conclude the computation of the…

We solve the conformal bootstrap equations of the four fermi model or $O(N)$ Gross Neveu model to deduce the fermion anomalous dimension of the theory at $O(1/N^3)$ in arbitrary dimensions.

We reformulate the Thirring model in $D$ $(2 \le D < 4)$ dimensions as a gauge theory by introducing $U(1)$ hidden local symmetry (HLS) and study the dynamical mass generation of the fermion through the Schwinger-Dyson (SD) equation. By…

In this work, we investigate a very important but unstressed result in the work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton ( J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have calculated the vacuum energy…

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a…

We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behavior. The conjecture is verified for free fermions, Heisenberg and quantum Ising ladders. Our results…