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Register a new userInfrared dressing in real time: emergence of anomalous dimensions
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We implement a dynamical resummation method (DRM) as an extension of the dynamical renormalization group to study the time evolution of infrared dressing in non-gauge theories. Super renormalizable and renormalizable models feature infrared divergences similar to those of a theory at a critical point, motivating a renormalization group improvement of the propagator that yields a power law decay of the survival probability $propto t^{-Delta}$. The (DRM) confirms this decay, yields the dressed state and determines that the anomalous dimension $Delta$ is completely determined by the slope of the spectral density at threshold independent of the ultraviolet behavior, suggesting certain universality for infrared phenomena. The dressed state is an entangled state of the charged and massless quanta. The entanglement entropy is obtained by tracing over the unobserved massless quanta. Its time evolution is determined by the (DRM), it is infrared finite and describes the information flow from the initial single particle to the asymptotic multiparticle dressed state. We show that effective field theories of massless axion-like particles coupled to fermion fields do not feature infrared divergences, and provide a criterion for infrared divergences in effective field theories valid for non-gauge theories up to one loop.
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Quantum Darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment. It was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics, whenever the system of interest has finite dimensions and the number of environment fragments is large [F. G. S. L. Brand~ao, M. Piani, and P. Horodecki, Nature Commun. 6, 7908 (2015)]. Despite the importance of this result, it necessarily excludes many practical systems of interest that are infinite-dimensional, including harmonic oscillators. Extending the study of Quantum Darwinism to infinite dimensions is a nontrivial task: we tackle it here by using a modified diamond norm, suitable to quantify the distinguishability of channels in infinite dimensions. We prove two theorems that bound the emergence of objectivity, first for finite energy systems, and then for systems that can only be prepared in states with an exponential energy cut-off. We show that the latter class of states includes any bounded-energy subset of single-mode Gaussian states.
We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to $O(Delta_f^3)$, where $Delta_f$ is an $N_f$-dependent expansion variable. Our general results are evaluated for several special cases, including the case $G={rm SU}(N_c)$ with $R$ equal to the fundamental and adjoint representations.
In this article we study a nonlocal Nambu--Jona-Lasinio (nNJL) model with a Gaussian regulator in presence of a uniform magnetic field. We take a mixed approach to the incorporation of temperature in the model, and consider aspects of both real and imaginary time formalisms. We include confinement in the model through the quasiparticle interpretation of the poles of the propagator. The effect of the magnetic field in the deconfinement phase transition is then studied. It is found that, like with chiral symmetry restoration, magnetic catalysis occurs for the deconfinement phase transition. It is also found that the magnetic field enhances the thermodynamical instability of the system. We work in the weak field limit, i.e. $(eB)<5m_pi^2$. At this level there is no splitting of the critical temperatures for chiral and deconfinement phase transitions.
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable truncation schemes for real-time calculations as well as the numerical procedure to self-consistently solve the flow equations for the spectral function. Subsequently, we discuss the relations to other perturbative and non-perturbative approaches to calculate spectral functions, and present a detailed comparison and benchmark in $d=0+1$ dimensions.
We compute the spectrum of anomalous dimensions of non-derivative composite operators with an arbitrary number of fields $n$ in the $O(N)$ vector model with cubic anisotropy at the one-loop order in the $epsilon$-expansion. The complete closed-form expression for the anomalous dimensions of the operators which do not undergo mixing effects is derived and the structure of the general solution to the mixing problem is outlined. As examples, the full explicit solution for operators with up to $n=6$ fields is presented and a sample of the OPE coefficients is calculated. The main features of the spectrum are described, including an interesting pattern pointing to the deeper structure.
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