100 research outputs found
Comments on ``A note on first-order formalism and odd-derivative actions'' by S. Deser
We argue that the obstacles to having a first-order formalism for
odd-derivative actions presented in a pedagogical note by Deser are based on
examples which are not first-order forms of the original actions. The general
derivation of an equivalent first-order form of the original second-order
action is illustrated using the example of topologically massive
electrodynamics (TME). The correct first-order formulations of the TME model
keep intact the gauge invariance presented in its second-order form
demonstrating that the gauge invariance is not lost in the Ostrogradsky
process.Comment: 6 pages, references are adde
Ostrogradsky's Hamilton formalism and quantum corrections
By means of a simple scalar field theory it is demonstrated that the Lagrange
formalism and Ostrogradsky's Hamilton formalism in the presence of higher
derivatives, in general, do not lead to the same results. While the two
approaches are equivalent at the classical level, differences appear due to the
quantum corrections.Comment: 10 pages, 1 figure, REVTeX
On Hamiltonian formulation of the Einstein-Hilbert action in two dimensions
It is shown that the well-known triviality of the Einstein field equations in
two dimensions is not a sufficient condition for the Einstein-Hilbert action to
be a total divergence, if the general covariance is to be preserved, that is, a
coordinate system is not fixed. Consequently, a Hamiltonian formulation is
possible without any modification of the two dimensional Einstein-Hilbert
action. We find the resulting constraints and the corresponding gauge
transfromations of the metric tensor.Comment: 9 page
Spontaneously scalarized Kerr black holes in extended scalar-tensor-Gauss-Bonnet gravity
We construct asymptotically flat, spinning, regular on and outside an event horizon, scalarized black holes (SBHs) in extended scalar-tensor-Gauss-Bonnet models. They reduce to Kerr BHs when the scalar field vanishes. For an illustrative choice of nonminimal coupling, we scan the domain of existence. For each value of spin, SBHs exist in an interval between two critical masses, with the lowest one vanishing in the static limit. Non-uniqueness with Kerr BHs of equal global charges is observed; the SBHs are entropically favoured. This suggests that SBHs form dynamically from the spontaneous scalarization of Kerr BHs, which are prone to a scalar-triggered tachyonic instability, below the largest critical mass. Phenomenologically, the introduction of BH spin damps the maximal observable difference between comparable scalarized and vacuum BHs. In the static limit, (perturbatively stable) SBHs can store over 20% of the spacetime energy outside the event horizon; in comparison with Schwarzschild BHs, their geodesic frequency at the ISCO can differ by a factor of 2.5 and deviations in the shadow areal radius may top 40%. As the BH spin grows, low mass SBHs are excluded, and the maximal relative differences decrease, becoming of the order of a few percent for dimensionless spin j≳0.5. This reveals a spin selection effect: non-GR effects are only significant for low spin. We discuss if and how the recently measured shadow size of the M87 supermassive BH constrains the length scale of the Gauss-Bonnet coupling.publishe
Quark mass correction to the string potential
A consistent method for calculating the interquark potential generated by the
relativistic string with massive ends is proposed. In this approach the
interquark potential in the model of the Nambu--Goto string with point--like
masses at its ends is calculated. At first the calculation is done in the
one--loop approximation and then the variational estimation is performed. The
quark mass correction results in decreasing the critical distance
(deconfinement radius). When quark mass decreases the critical distance also
decreases. For obtaining a finite result under summation over eigenfrequencies
of the Nambu--Goto string with massive ends a suitable mode--by--mode
subtraction is proposed. This renormalization procedure proves to be completely
unique. In the framework of the developed approach the one--loop interquark
potential in the model of the relativistic string with rigidity is also
calculated.Comment: 34 pages, LATE
Perturbative Hamiltonian constraints for higher order theories
We present a method for constructing a consistent low energy canonical
formalism for higher order time-derivative theories, extending the Dirac method
to include perturbative Hamiltonian constraints. We apply it to two
paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan
scalar field. We also compare the results, both at the classical and quantum
level, with the ones corresponding to a direct perturbative construction
applied to the exact higher order theory. This comparison highligths the
soundness of the present formalism.Comment: 26 pages, 4 figures; review section shortened and appendices change
The Matsubara-Fradkin Thermodynamical Quantization of Podolsky Electrodynamics
In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's
auxiliary field method to the quantization of the Podolsky electrodynamics in
thermodynamic equilibrium. This approach allows us to write consistently the
path integral representation for the partition function of gauge theories in a
simple manner. Furthermore, we find the Dyson-Schwinger-Fradkin equations and
the Ward-Fradkin-Takahashi identities for the Podolsky theory. We also write
the most general form for the polarization tensor in thermodynamic equilibrium.Comment: Submitted to Physical Review
Cleaning up the cosmological constant
We present a novel idea for screening the vacuum energy contribution to the
overall value of the cosmological constant, thereby enabling us to choose the
bare value of the vacuum curvature empirically, without any need to worry about
the zero-point energy contributions of each particle. The trick is to couple
matter to a metric that is really a composite of other fields, with the
property that the square-root of its determinant is the integrand of a
topological invariant, and/or a total derivative. This ensures that the vacuum
energy contribution to the Lagrangian is non-dynamical. We then give an
explicit example of a theory with this property that is free from Ostrogradski
ghosts, and is consistent with solar system physics and cosmological tests.Comment: 8 pages, typos corrected and more text added, version accepted for
publication in JHE
Equivalence of Hamiltonian and Lagrangian Path Integral Quantization: Effective Gauge Theories
The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev--Popov)
path integral quantization (Matthews's theorem) is proven for gauge theories
with arbitrary effective interaction terms. Effective gauge-boson
self-interactions and effective interactions with scalar and fermion fields are
considered. This result becomes extended to effective gauge theories with
higher derivatives of the fields.Comment: 14 pages LaTeX, BI-TP 93/40, August 199
Effective Lagrangians with Higher Order Derivatives
The problems that are connected with Lagrangians which depend on higher order
derivatives (namely additional degrees of freedom, unbound energy from below,
etc.) are absent if effective Lagrangians are considered because the equations
of motion may be used to eliminate all higher order time derivatives from the
effective interaction term. The application of the equations of motion can be
realized by performing field transformations that involve derivatives of the
fields. Using the Hamiltonian formalism for higher order Lagrangians
(Ostrogradsky formalism), Lagrangians that are related by such transformations
are shown to be physically equivalent (at the classical and at the quantum
level). The equivalence of Hamiltonian and Lagrangian path integral
quantization (Matthews's theorem) is proven for effective higher order
Lagrangians. Effective interactions of massive vector fields involving higher
order derivatives are examined within gauge noninvariant models as well as
within (linearly or nonlinearly realized) spontaneously broken gauge theories.
The Stueckelberg formalism, which relates gauge noninvariant to gauge invariant
Lagrangians, becomes reformulated within the Ostrogradsky formalism.Comment: 17 pages LaTeX, BI-TP 93/2
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