arXiv subjects

F. T. Brandt

Publications and source records attributed to F. T. Brandt.

At least 55 records · Page 3Linked to original sources

arXiv2011

Electrodynamics in a Background Chiral Field

We consider the one loop effective action in four dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass $m$ of the spinor vanishes. If $m$ does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.

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arXiv2011

Non-Quadratic Gauge Fixing and Ghosts for Gauge Theories on the Hypersphere

It has been suggested that using a gauge fixing Lagrangian that is not quadratic in a gauge fixing condition is most appropriate for gauge theories formulated on a hypersphere. We reexamine the appropriate ghost action that is to be associated with gauge fixing, applying a technique that has been used for ensuring that the propagator for a massless spin-two field is transverse and traceless. It is shown that this non-quadratic gauge fixing Lagrangian leads to two pair of complex Fermionic ghosts and two Bosonic real ghosts.

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arXiv2010

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory (BET) approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially non-perturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with non-trivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.

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arXiv2010

Quantum statistical correlations in thermal field theories: boundary effective theory

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field $ϕ_c$, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrödinger field-representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field $ϕ_c$, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example.

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arXiv2009

Resummation of infrared divergences in the free-energy of spin-two fields

We derive a closed form expression for the sum of all the infrared divergent contributions to the free-energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing non-interacting spin two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free-energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.

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arXiv2009

Non-Quadratic Gauge Fixing and Global Gauge Invariance in the Effective Action

The possibility of having a gauge fixing term in the effective Lagrangian that is not a quadratic expression has been explored in spin-two theories so as to have a propagator that is both traceless and transverse. We first show how this same approach can be used in spontaneously broken gauge theories as an alternate to the 't Hooft gauge fixing which avoids terms quadratic in the scalar fields. This "non-quadratic" gauge fixing in the effective action results in there being two complex Fermionic and one real Bosonic ghost fields. A global gauge invariance involving a Fermionic gauge parameter, analogous to the usual BRST invariance, is present in this effective action.

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arXiv2008

Thermal instability in a gravity-like scalar theory

We study the question of stability of the ground state of a scalar theory which is a generalization of the phi^3 theory and has some similarity to gravity with a cosmological constant. We show that the ground state of the theory at zero temperature becomes unstable above a certain critical temperature, which is evaluated in closed form at high temperature.

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arXiv2008

Instabilities in Thermal Gravity with a Cosmological Constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature.

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arXiv2007

Fermionic Contributions to the Free Energy of Noncommutative Quantum Electrodynamics at High Temperature

We consider the fermionic contributions to the free energy of noncommutative QED at finite temperature $T$. This analysis extends the main results of our previous investigation where we have considered the pure bosonic sector of the theory. For large values of $θT^2$ ($θ$ is the magnitude of the noncommutative parameters) the fermionic contributions decrease the value of the critical temperature, above which there occurs a thermodynamic instability.

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arXiv2006

The Effective Potential in the Massive $ϕ_4^4$ Model

By applying the renormalization group equation, it has been shown that the effective potential $V$ in the massless $ϕ_4^4$ model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive $ϕ_4^4$ model, showing that the effective potential is independent of $ϕ$ here as well.

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arXiv2006

On the Free Energy of Noncommutative Quantum Electrodynamics at High Temperature

We compute higher order contributions to the free energy of noncommutative quantum electrodynamics at a nonzero temperature $T$. Our calculation includes up to three-loop contributions (fourth order in the coupling constant $e$). In the high temperature limit we sum all the {\it ring diagrams} and obtain a result which has a peculiar dependence on the coupling constant. For large values of $eθT^2$ ($θ$ is the magnitude of the noncommutative parameters) this non-perturbative contribution exhibits a non-analytic behavior proportional to $e^3$. We show that above a certain critical temperature, there occurs a thermodynamic instability which may indicate a phase transition.

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arXiv2006

Scalar-graviton interaction in the noncommutative space

We obtain the leading order interaction between the graviton and the neutral scalar boson in the context of noncommutative field theory. Our approach makes use of the Ward identity associated with the invariance under a subgroup of symplectic diffeomorphisms.

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arXiv2006

Thermal Operator and Cutting Rules at Finite Temperature and Chemical Potential

In the context of scalar field theories, both real and complex, we derive the cutting description at finite temperature (with zero/finite chemical potential) from the cutting rules at zero temperature through the action of a simple thermal operator. We give an alternative algebraic proof of the largest time equation which brings out the underlying physics of such a relation. As an application of the cutting description, we calculate the imaginary part of the one loop retarded self-energy at zero/finite temperature and finite chemical potential and show how this description can be used to calculate the dispersion relation as well as the full physical self-energy of thermal particles.

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arXiv2005

The renormalization group improved effective potential in massless models

The effective potential $V$ is considered in massless $λϕ^4_4$ theory. The expansion of $V$ in powers of the coupling $λ$ and of the logarithm of the background field $ϕ$ is reorganized in two ways; first as a series in $λ$ alone, then as a series in $\lnϕ$ alone. By applying the renormalization group (RG) equation to $V$, these expansions can be summed. Using the condition $V^\prime(v) = 0$ (where $v$ is the vacuum expectation value of $ϕ$) in conjunction with the expansion of $V$ in powers of $\lnϕ$ fixes $V$ provided $v\neq 0$. In this case, the dependence of $V$ on $ϕ$ drops out and $V$ is not analytic in $λ$. Massless scalar electrodynamics is considered using the same approach.

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arXiv2003

Transport equation for the photon Wigner operator in non-commutative QED

We derive an exact quantum equation of motion for the photon Wigner operator in non-commutative QED, which is gauge covariant. In the classical approximation, this reduces to a simple transport equation which describes the hard thermal effects in this theory. As an example of the effectiveness of this method we show that, to leading order, this equation generates in a direct way the Green amplitudes calculated perturbatively in quantum field theory at high temperature.

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arXiv2003

Thermal one- and two-graviton Green's functions in the temporal gauge

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.

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arXiv2003

The static effective action for non-commutative QED at high temperature

In this paper, we systematically study the effective action for non-commutative QED in the static limit at high temperature. When $θp^{2}\ll 1$, where $θ$ represents the magnitude of the parameter for non-commutativity and $p$ denotes a typical external three momentum, we show that this leads naturally to a derivative expansion in this model. The study of the self-energy, in this limit, leads to nontrivial $θ$ dependent corrections to the electric and magnetic masses, which exist only above a certain critical temperature. The three point and the four point amplitudes are also studied as well as their relations to the Ward identities in this limit. We determine the closed form expression for the current involving only the spatial components of the gauge field and present the corresponding static effective action, which is gauge invariant.

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arXiv2002

The open superstring 5-point amplitude revisited

We derive the complete five-gluon scattering amplitude at tree level, within the context of Open Superstring theory. We find the general expression in terms of kinematic factors, and also find its complete expansion up to ${\cal O}({α'}^3)$ terms. We use our scattering amplitude to test three non-equivalent ${\cal O}({α'}^3)$ effective lagrangians that have recently been matter of some controversy.

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