General modular quantum dilogarithm and beta intergals

**field**

**theory**on the general squashed lens space. Possible applications to $2d$ conformal

**field**

**theory**are briefly discussed as well.

4/10 relevant

arXiv

The $B\to \pi \ell\nu_\ell$ semileptonic decay within the LCSR approach
under heavy quark effective **field** **theory**

**field**

**theory**(HQEFT) provides an effective way to deal with the heavy meson decays. In the paper, we adopt two different correlators to derive the light-cone sum rules of the $B \to \pi$ transition form factors (TFFs) within the framework of HQEFT. We label those two LCSR results as LCSR-${\cal U}$ and LCSR-${\cal R}$, which are for conventional correlator and right-handed correlator, respectively. We observe that the correlation parameter $|\rho_{\rm RU}|$ for the branching ratio ${\cal B}(B \to \pi l \nu_{l})$ is $\sim 0.85$, implying the consistency of the LCSRs under different correlators. Moreover, we obtain $|V_{\rm ub}|_{{\rm LCSR}-{\cal U}}=(3.45^{+0.28}_{-0.20}\pm{0.13}_{\rm{exp}})\times10^{-3}$ and $|V_{\rm ub}|_{{\rm LCSR}-{\cal R}} =(3.38^{+0.22}_{-0.16} \pm{0.12}_{\rm{exp}})\times10^{-3}$. We then obtain $\mathcal{R}_{\pi}|_{{\rm LCSR}-{\cal U}}=0.68^{+0.10}_{-0.09}$ and $\mathcal{R}_{\pi}|_{{\rm LCSR}-{\cal R}}=0.65^{+0.13}_{-0.11}$, both of them agree with the Lattice QCD predictions. Thus the HQEFT provides a useful framework for studying the $B$ meson decays. Moreover, by using right-handed correlator, the twist-2 terms shall dominant the TFF $f^+(q^2)$, which approaches over $\sim97\%$ contribution in the whole $q^2$-region; and the large twist-3 uncertainty for the conventional correlator is greatly suppressed. One can thus adopt the LCSR-${\cal R}$ prediction to test the properties of the various models for the pion twist-2 distribution amplitudes.

10/10 relevant

arXiv

Conservation laws generated by symmetry transformations of extremals and
applications in Lagrangian **field** **theory**

7/10 relevant

arXiv

Chiral magnetic effect at finite temperature in a **field**-theoretic
approach

**field**

**theory**, regularized via zeta functions. Expand abstract.

**field**theory, regularized via zeta functions. We show that the effect only appears when the manifold is finite in the direction of the magnetic

**field**and, in this case, it does depend on the temperature, a well as on the size of the sample in the direction of the magnetic field, even for a temperature-independent chiral chemical potential. Indeed, the associated current agrees with the result usually quoted only in the zero-temperature limit, while it decreases with the temperature.

4/10 relevant

arXiv

Gribov ambiguity

**field**

**theory**. Expand abstract.

**theory**by imposing the covariant gauge constraint. Unfortunately, the solution of the gauge constraint is not unique, thus the redundant gauge degree of freedom, called Gribov copies, remains unfixed. One of the traditional methods to partially resolve the Gribov problem is to restrict the space of gauge orbits inside the bounded region known as the Gribov region. The meaning of partially resolve is that this procedure can solve only the positivity's problem of the Faddeev-Popov operator but the Gribov copies are still there. However, on the bright side, the restriction to the Gribov region leads to the modification of the gluon propagator. Additionally, the new form of the gluon propagator yields the violation of the reflection positivity which is considered as the important axiom of the Euclidean quantum

**field**

**theory**. This shows that the gluon

**field**in the Gribov region is an unphysical particle or technically confined. In this review article, we will start by discussing the traditional Faddeev-Popov method and its consequence on the proof of the unitarity of the perturbative Yang-Mills

**theory**. Next, we will discuss the blind spot of the Faddeev-Popov quantization and study the mathematical and physical origin of the Gribov problem. Then, the method of the Gribov restriction will be elaborated. After that, we demonstrate the modification of the gluon

**field**after restricting inside the bounded Gribov region. Finally, we show that the new form of the gluon leads to the violation of the reflection positivity axiom.

4/10 relevant

arXiv

Unstable states in a model of nonrelativistic quantum electrodynamics: rate of decay, regeneration by decay products, sojourn time and irreversibility

**field**theoretic, i.e., not present in nonrelativistic Schroedinger quantum mechanics. Some implications of this fact are analysed from the point of view of a general picture of irreversibility and the "arrow of time" in quantum

**field**

**theory**. Finally, we make a first application of a time-energy uncertainty theorem to a quantum

**field**theoretic model, in order to find a lower bound to the energy fluctuation in the state $\Psi$ (Theorem 5.2). In the process, it is also suggested that the time of sojourn $\tau_{H}(\Psi)= \int_{0}^{\infty} |R_{\Psi}(t)|^{2}dt$ is the most natural quantity to consider in connection with the decay of unstable atoms or particles: it is proved to coincide with the the average lifetime of the decaying state, a standard quantity in quantum probability. No use is made of complex energies associated to analytic continuations of the resolvent operator to "unphysical" Riemann sheets.

4/10 relevant

arXiv

The Dynamic Ligand **Field** of a Molecular Qubit: Decoherence Through Spin–Phonon Coupling

**field**

**theory**model to describe and quantify the nature of spin–phonon coupling terms in S = 1/2 transition metal complexes. Expand abstract.

**field**contributions has not been established. Here we derive a general ligand

**field**

**theory**model to describe and quantify the nature of spin–phonon coupling terms in S = 1/2 transition metal complexes. We show that the coupling term for a given vibrational mode is governed by: 1) the magnitude of the metal-based spin–orbit coupling constant, 2) the magnitude and gradient in the ligand

**field**excited state energy, and 3) dynamic relativistic nephelauxetic contributions reflecting the magnitude and gradient in the covalency of the ligand–metal bonds. From an extensive series of density functional

**theory**(DFT) and time-dependent DFT (TDDFT) calculations calibrated to a range of experimental data, spin–phonon coupling terms describing minimalistic D4h/D2d [CuCl4]2- and C4v [VOCl4]2- complexes translate to and correlate with experimental quantum coherence properties observed for Cu(II)- and V(IV)-based molecular qubits with different ligand sets, geometries, and coordination numbers. While providing a fundamental framework and means to benchmark current qubits, the model and methodology described herein can be used to screen any S = 1/2 molecular qubit candidate and guide the discover of room temperature coherent materials for quantum information processing.

4/10 relevant

chemRxiv

Complexity for Charged Thermo**field** Double States

**field**

**theory**in the presence of background electric

**field**. We show that the ratio of the complexity of formation for cTFD state to the thermodynamic entropy is finite and it depends just on the temperature and chemical potential. Moreover, this ratio smoothly approaches the value for real scalar

**theory**. We compare our

**field**

**theory**calculations with holographic complexity of charged black holes and confirm that the same cost function which is used for neutral case continues to work in presence of $U(1)$ background

**field**. For $t>0$, the complexity of cTFD state evolves in time and contrasts with holographic results, it saturates after a time of the order of inverse temperature. This discrepancy can be understood by the fact that holographic QFTs are actually strong interacting theories, not free ones.

4/10 relevant

arXiv

Fusion and positivity in chiral conformal **field** **theory**

**field**

**theories**, both of which have had a significant impact on related mathematical areas of study. Expand abstract.

**field**theories, both of which have had a significant impact on related mathematical areas of study. The two settings are expected to be equivalent under suitable hypotheses, but in practice such an equivalence has proven elusive, especially with regard to fusion products. This article develops a framework for the systematic comparison of fusion products between the contexts of VOAs and conformal nets. This framework is based on the geometric technique of 'bounded localized vertex operators,' which realizes algebras of observables via insertion operators localized in partially thin Riemann surfaces. We apply our framework to solve old problems about conformal nets and subfactors (e.g. rationality of all WZW conformal nets), obtain new results about VOAs (e.g. unitarity of representation categories), and give short proofs of many old results. We also consider a general class of positivity phenomena for VOAs, and use this to outline a program for identifying unitary tensor product

**theories**of VOAs and conformal nets even for badly-behaved models.

8/10 relevant

arXiv

Sir Michael Atiyah, a Knight Mathematician A tribute to Michael Atiyah, an inspiration and a friend

**theory**together with the Atiyah-Singer index theorem for which he received

**Fields**Medal (1966). Expand abstract.

**theory**together with the Atiyah-Singer index theorem for which he received

**Fields**Medal (1966). He received also the Abel Prize (2004) along with Isadore M. Singer for their discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics. Indeed, his work has helped theoretical physicists to advance their understanding of quantum

**field**

**theory**and general relativity.

4/10 relevant

arXiv