Results 1 - 10 of 4492
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[en] Coset methods are used to construct the action describing the dynamics of the (massive) Nambu-Goldstone scalar degree of freedom associated with the spontaneous breaking of the isometry group of AdSd+1 space to that of an AdSd subspace. The resulting action is an SO(2,d) invariant AdS generalization of the Nambu-Goto action. The vector field theory equivalent action is also determined
[en] In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the full range of the parameters, using both topological and geometrical methods. In particular, we show that the given parametrization realizes the group SU(N+1) as a fibration of U(N) over the complex projective space CPn. This justifies the interpretation of the parameters as generalized Euler angles
[en] Here, a brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators—and corresponding EOS constraints—otherwise appearing in the existing literature are recovered through the application and invariance under Lie derivative dragging operations.
[en] We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables. Such expectations can be estimated by performing projective measurements on (M3log(M/δ)/ε2) copies of the state, where M is the dimension of an associated Lie algebra, ε is a precision parameter, and 1 - δ is the required confidence level. The method can be implemented on a classical computer and runs in time (M4log(M/ε)). It provides (Mlog(M/ε)) simple unitaries that form the sequence. The overall complexity is then polynomial in M, being very efficient in cases where M is significantly smaller than the Hilbert space dimension, as for some fermion algebras. When the algebra of relevant observables is given by certain Pauli matrices, each simple unitary may be easily decomposed into two-qubit gates. We discuss applications to efficient quantum state tomography and classical simulations of quantum circuits.
[en] In this paper we present a construction for the compact form of the exceptional Lie group E6 by exponentiating the corresponding Lie algebra e6, which we realize as the sum of f4, the derivations of the exceptional Jordan algebra J3 of dimension 3 with octonionic entries, and the right multiplication by the elements of J3 with vanishing trace. Our parameterization is a generalization of the Euler angles for SU(2) and it is based on the fibration of E6 via a F4 subgroup as the fiber. It makes use of a similar construction we have performed in a previous article for F4. An interesting first application of these results lies in the fact that we are able to determine an explicit expression for the Haar invariant measure on the E6 group manifold
[en] In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e., the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we need the knowledge of the future of the path) and non-anticipative versions of the stochastic process. We obtain the anticipative description thanks to the theory of generalized Gaussian bridges while the non-anticipative representation comes from the theory of stochastic control. For this last representation, a stochastic differential equation is derived which leads to an effective Langevin equation. Finally, we extend our theoretical findings to linear bridge processes. (author)
[en] We provide a simple parameterization for the group G2, which is analogous to the Euler parameterization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H
[en] The “method” in question"1 has repeatedly led to results which I proved false in 1996 by a short, transparent, and rigorous theorem."2 Even shorter is the remark here that inspection of the standard formula for the electromagnetic field suffices to prove the results of the “method” false.
[en] The Feynman rules assign to every graph an integral which can be written as a function of a scaling parameter L. Assuming L for the process under consideration is very small, so that contributions to the renormalization group are small, we can expand the integral and only consider the lowest orders in the scaling. The aim of this article is to determine specific combinations of graphs in a scalar quantum field theory that lead to a remarkable simplification of the first non-trivial term in the perturbation series. It will be seen that the result is independent of the renormalization scheme and the scattering angles. To achieve that goal we will utilize the parametric representation of scalar Feynman integrals as well as the Hopf algebraic structure of the Feynman graphs under consideration. Moreover, we will present a formula which reduces the effort of determining the first-order term in the perturbation series for the specific combination of graphs to a minimum.
[en] The BPS Skyrme model is a model containing an SU(2)-valued scalar field, in which a Bogomol’nyi-type inequality can be satisfied by soliton solutions (skyrmions). In this model, the energy density of static configurations is the sum of the square of the topological charge density plus a potential. The topological charge density is nothing else but the pull-back of the Haar measure of the group SU(2) on the physical space by the field configuration. As a consequence, this energy expression has a high degree of symmetry: it is invariant to volume preserving diffeomorphisms both on physical space and on the target space. We demonstrate here that in the BPS Skyrme model such solutions exist that a fraction of its charge and energy densities is localised, and the remaining part can be far away, not interacting with the localised part.