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The loss of particles due to highly inelastic reactions has previously been taken into account in effective field theories for low-energy particles by adding local anti-Hermitian terms to the effective Hamiltonian. An additional modification is required in the time evolution equation for the density matrix of a multi-particle system. An effective density matrix can be defined by tracing over states containing high-momentum particles produced by the highly inelastic reactions and by a time average that eliminates short-time correlations. The effective density matrix satisfies the Lindblad equation, with local Lindblad operators that are determined by the anti-Hermitian terms in the effective Hamiltonian.
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Effective field theories have often been applied to systems with deeply inelastic reactions that produce particles with large momenta outside the domain of validity of the effective theory. The effects of the deeply inelastic reactions have been taken into account in previous work by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-particle systems are considered, an additional modification is required in equations governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum particles, and show that it satisfies a Lindblad equation, with local Lindblad operators determined by the anti-Hermitian terms in the effective Hamiltonian density.
I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE coefficients of minimal-twist operators of even spin s geq 2. In the case of s=2, when the leading-twist operator is the stress tensor, we reproduce the Hofman-Maldacena bounds. For s>2 the bounds are new.
In this document, we briefly introduce the effective field theories. We propose some novel ideas in this manuscript. We introduce a novel formalism of the effective field theories and we apply it to the effective field theories of large scale structures. The new formalism is based on functionals of the actions composing those theories. We discuss our findings in a Cosmological Gravitology framework. We present with a cosmological inference approach these results and we give a guideline of how we can disentangle the best candidate between those models with some latest understanding of model selection.
The invariance of physical observables under redefinitions of the quantum fields is a well-known and important property of quantum field theory. We study perturbative field redefinitions in effective theories, paying special attention to higher-order effects and their impact on matching to an ultraviolet theory at the classical and quantum levels.
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