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Multiplicative logarithmic corrections frequently characterize critical behaviour in statistical physics. Here, a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when…
Uniform random exploration in decision-making systems supports off-policy learning via supervision but incurs high regret, making it impractical for many applications. Conversely, non-uniform exploration offers better immediate performance…
The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in…
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target…
We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…
Perturbative estimates of operator coefficients for improved lattice actions are becoming increasingly important for precision simulations of many hadronic observables. Following previous work by Dimm, Lepage, and Mackenzie, we consider the…
We give a formula for the derivatives of a correlation function of composite operators with respect to the parameters (i.e., the strong fine structure constant and the quark mass) of QCD in four-dimensional euclidean space. The formula is…
We study the high-energy small-angle {\it Regge} limit of the fermion-antifermion scattering in gauge theories and consider the part of the amplitude suppressed by a power of the scattering angle. For abelian gauge group all-order…
Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the $1/N_c$ expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon…
The field-theoretic renormalization group (RG) and the operator product expansion are applied to the model of a divergence-free vector quantity, passively advected by the ``synthetic'' turbulent flow with a finite correlation time. The…
A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of…
The time evolution of local operators in quantum compass models is characterized by simplicity as it can be represented as expanding and contracting strings of operators. Here we present an analytical solution to the problem of growth of a…
The theoretical description of fermions in the presence of Lorentz and CPT violation is developed. We classify all Lorentz- and CPT-violating and invariant terms in the quadratic Lagrange density for a Dirac fermion, including operators of…
A new method to study the retardation effects in mesons is presented. Inspired from the covariant oscillator quark model, it is applied to the rotating string model in which a non zero value is allowed for the relative time between the…
We analyze the heavy quark bound state spectrum using an order-dependent conformal mapping to re-sum the perturbative expansion for current correlators. The procedure consists of two main steps. Firstly, the Borel plane structure of the…
Starting with the first-order singular Lagrangian describing the dynamical system with 2nd-class constraints, the noncommutative quantum mechanics on a curved space is investigated by the constraint star-product quantization formalism of…
We explore a new way of probing scattering of closed strings in $AdS_5\times S^5$, which we call `the large $p$ limit'. It consists of studying four-point correlators of single-particle operators in $\mathcal{N}=4$ SYM at large $N$ and…
The equation of state and, more generally, the thermodynamics of the Lennard-Jones fluid have long served as a benchmark problem in the statistical theory of fluids. Among available theoretical approaches, first-order perturbation theory…
In these lectures, we present the behavior of conventional $\bar{q}q$ mesons, glueballs, and hybrids in the large-$N_{c}$ limit of QCD. To this end, we use an approach based on rather simple NJL-like bound-state equations. The obtained…
The Zygmund vector field maximal function conjecture is a long-standing open problem. This paper establishes a new boundedness criterion that significantly weakens the existing conditions in the literature. Specifically, the required decay…