arXiv subjects

Paulo R. S. Carvalho

Publications and source records attributed to Paulo R. S. Carvalho.

11 recordsLinked to original sources

arXiv2020

Ramsey interferometry as a witness of acceleration radiation

We adapt a typical Ramsey interferometer by inserting a linear accelerator capable of accelerating an atom inside a single-mode cavity. We demonstrate that this simple scheme allows us to estimate the effects of acceleration radiation via interferometric visibility. By using a Rydberg-like atom, our results suggest that, for the transition regime of the order of GHz and interaction time of 1 ns, acceleration radiation effects can be observable for accelerations as low as $10^{17}$ m/s$^2$.

quant-ph↗

arXiv2020

Alice and Bob in an anisotropic expanding spacetime

We investigate a quantum teleportation process between two comoving observers Alice and Bob in an anisotropic expanding spacetime. In this model, we calculate the fidelity of teleportation and we noted an oscillation of its spectrum as a function of the azimuthal angle. We found that for the polar angle $ϕ= \fracπ{2}$ and the azimuthal angle $θ\neq \frac{3π}{4} + nπ$ with $n = 0, 1, 2, ...$ the efficiency of the process decreases, i.e., the fidelity is less than one. In addition, it is shown that the anisotropic effects on the fidelity becomes more significative in the regime of smooth expansion and the limit of massless particles. On the other hand, the influence of curvature coupling becomes noticeable in the regime of fast expansion (values of $\fracρω \gg 1$).

hep-th↗

arXiv2017

Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann: massive scalar theory and critical exponents

We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar $λϕ^{4}$ theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents $η$ and $ν$ at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann ($BPHZ$) method at the same loop order, show that the proposed method requires fewer diagrams and establish a connection between the two approaches.

hep-th↗

arXiv2015

Renormalization group approach for Lorentz-violating scalar field theory at all loop orders

We compute, both explicitly up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O($N$) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is eeded. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. At the end we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.

hep-th↗

arXiv2015

All-loop order critical exponents for massless scalar field theory with Lorentz violation in the BPHZ method

We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating O($N$) self-interacting $λϕ^{4}$ scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading order and later in a proof by induction up to any loop level, the respective $β$-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.

hep-th↗

arXiv2015

Robustness of the O($N$) universality class

We calculate the critical exponents for Lorentz-violating O($N$) $λϕ^{4}$ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An identical task is fulfilled in the second case in a massive version of the same theory, previously renormalized in the BPHZ method in four dimensions. We show that although the renormalization constants, the $β$ and anomalous dimensions acquire Lorentz-violating quantum corrections, the outcome for the critical exponents in both methods are identical and furthermore they are equal to their Lorentz-invariant counterparts. Finally we generalize the last two results for all loop levels and we provide symmetry arguments for justifying the latter.

hep-th↗

arXiv2014

Three-loop field renormalization for scalar field theory with Lorentz violation

Applying the counterterm method in minimal subtraction scheme we calculate the three-loop quantum correction to field anomalous dimension in a Lorentz-violating O($N$) self-interacting scalar field theory. We compute the Feynman diagrams using dimensional regularization and $ε$-expansion techniques. As this approximation corresponds to a three-loop term, to our knowledge this is the first time in literature in which such a loop level is attained for a LV theory.

hep-th↗

arXiv2014

Mass Renormalization in Lorentz-violating Scalar Field Theory

In this work we evaluate the $γ_{m}$ function corresponding to mass renormalization for O($N$) scalar field theory with Lorentz violation. We calculate this function up to two-loop order for a theory renormalized utilizing the counterterm method in the minimal subtraction scheme with Feynman diagrams regularized using dimensional regularization.

hep-th↗

arXiv2014

Massive minimal subtraction scheme and "partial-$p$" in anisotropic Lifshitz space(time)s

We introduce the "partial-$p$" operation in a massive Euclidean $λϕ^{4}$ scalar field theory describing anisotropic Lifshitz critical behavior. We then develop a minimal subtraction a la $Bogoliubov-Parasyuk-Hepp-Zimmermann$ renormalization scheme. As an application we compute critical exponents diagrammatically using the orthogonal approximation at least up to two-loop order and show their equivalence with other renormalization techniques. We discuss possible applications of the method in other field-theoretic contexts.

hep-th↗

arXiv2009

Callan-Symanzik-Lifshitz approach to generic competing systems

We present the Callan-Symanzik-Lifshitz method to approaching the critical behaviors of systems with arbitrary competing interactions. Every distinct competition subspace in the anisotropic cases define an independent set of renormalized vertex parts via normalization conditions with nonvanishing distinct masses at zero external momenta. Otherwise, only one mass scale is required in the isotropic behaviors. At the critical dimension, we prove: i) the existence of the Callan-Symanzik-Lifshitz equations and ii) the multiplicative renormalizability of the vertex functions using the inductive method. Away from the critical dimension, we utilize the orthogonal approximation to compute higher loop Feynman integrals, anisotropic as well as isotropic, necessary to get the exponents $η_{n}$ and $ν_{n}$ at least up to two-loop level. Moreover, we calculate the latter exactly for isotropic behaviors at the same perturbative order. Similarly to the computation in the massless formalism, the orthogonal approximation is found to be exact at one-loop order. The outcome for all critical exponents matches exactly with those computed using the zero mass field-theoretic description renormalized at nonvanishing external momenta.

hep-th↗

arXiv2007

Callan-Symanzik method for $m$-axial Lifshitz points

We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero external momenta. The orthogonal approximation is employed to obtain the critical indices $η_{L2}$, $ν_{L2}$, $η_{L4}$ and $ν_{L4}$ diagramatically at least up to two-loop order in the anisotropic criticalities. This approximation is also utilized to compute the exponents $η_{L4}$ and $ν_{L4}$ in the isotropic case. Furthermore, we compute those exponents exactly for the isotropic behaviors at the same loop order. The results obtained for all exponents are in perfect agreement with those previously derived in the massless theories renormalized at nonzero external momenta.

hep-th↗