4,567 research outputs found
Hamiltonian formulation of a class of constrained fourth-order differential equations in the Ostrogradsky framework
We consider a class of Lagrangians that depend not only on some
configurational variables and their first time derivatives, but also on second
time derivatives, thereby leading to fourth-order evolution equations. The
proposed higher-order Lagrangians are obtained by expressing the variables of
standard Lagrangians in terms of more basic variables and their time
derivatives. The Hamiltonian formulation of the proposed class of models is
obtained by means of the Ostrogradsky formalism. The structure of the
Hamiltonians for this particular class of models is such that constraints can
be introduced in a natural way, thus eliminating expected instabilities of the
fourth-order evolution equations. Moreover, canonical quantization of the
constrained equations can be achieved by means of Dirac's approach to
generalized Hamiltonian dynamics.Comment: 8 page
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
Covariant quantization of infinite spin particle models, and higher order gauge theories
Further properties of a recently proposed higher order infinite spin particle
model are derived. Infinitely many classically equivalent but different
Hamiltonian formulations are shown to exist. This leads to a condition of
uniqueness in the quantization process. A consistent covariant quantization is
shown to exist. Also a recently proposed supersymmetric version for half-odd
integer spins is quantized. A general algorithm to derive gauge invariances of
higher order Lagrangians is given and applied to the infinite spin particle
model, and to a new higher order model for a spinning particle which is
proposed here, as well as to a previously given higher order rigid particle
model. The latter two models are also covariantly quantized.Comment: 38 pages, Late
Aspects of Diffeomorphism Invariant Theory of Extended Objects
The structure of a diffeomorphism invariant Lagrangians for an extended
object W embedded in a bulk space M is discussed by following a close analogy
with the relativistic particle in electromagnetic field as a system that is
reparametrization-invariant. The current construction naturally contains,
relativistic point particle, string theory, and Dirac--Nambu--Goto Lagrangians
with Wess--Zumino terms. For Lorentzian metric field, the non-relativistic
theory of an integrally submerged W-brane is well defined provided that the
brane does not alter the background interaction fields. A natural time gauge is
fixed by the integral submergence (sub-manifold structure) within a Lorentzian
signature structure. A generally covariant relativistic theory for the
discussed brane Lagrangians is also discussed. The mass-shell constraint and
the Klein--Gordon equation are shown to be universal when gravity-like
interaction is present. A construction of the Dirac equation for the W-brane
that circumvents some of the problems associated with diffeomorphism invariance
of such Lagrangians by promoting the velocity coordinates into a non-commuting
gamma variables is presented.Comment: added references and minor format changes, 5 pages revtex4 style, no
figures, talk presented at the 3rd International Symposium on Quantum Theory
and Symmetries, and the Argonne Brane Dynamics Worksho
Quantum mechanics of higher derivative systems and total derivative terms
A general theory is presented of quantum mechanics of singular,
non-autonomous, higher derivative systems. Within that general theory, -th
order and -th order Lagrangians are shown to be quantum mechanically
equivalent if their difference is a total derivative.Comment: 14 pages, REVTeX, no figure
On singular Lagrangians affine in velocities
The properties of Lagrangians affine in velocities are analyzed in a
geometric way. These systems are necessarily singular and exhibit, in general,
gauge invariance. The analysis of constraint functions and gauge symmetry leads
us to a complete classification of such Lagrangians.Comment: AMSTeX, 22 page
Perturbative Approach to Higher Derivative and Nonlocal Theories
We review a perturbative approach to deal with Lagrangians with higher or
infinite order time derivatives. It enables us to construct a consistent
Poisson structure and Hamiltonian with only first time derivatives order by
order in coupling. To the lowest order, the Hamiltonian is bounded from below
whenever the potential is. We consider spacetime noncommutative field theory as
an example.Comment: 19 pages, Latex, reference adde
Hamiltonian Quantization of Effective Lagrangians with Massive Vector Fields
Effective Lagrangians containing arbitrary interactions of massive vector
fields are quantized within the Hamiltonian path integral formalism. It is
proven that correct Hamiltonian quantization of these models yields the same
result as naive Lagrangian quantization (Matthews's theorem). This theorem
holds for models without gauge freedom as well as for (linearly or nonlinearly
realized) spontaneously broken gauge theories. The Stueckelberg formalism, a
procedure to rewrite effective Lagrangians in a gauge invariant way, is
reformulated within the Hamiltonian formalism as a transition from a second
class constrained theory to an equivalent first class constrained theory. The
relations between linearly and nonlinearly realized spontaneously broken gauge
theories are discussed. The quartically divergent Higgs self interaction is
derived from the Hamiltonian path integral.Comment: 16 pages LaTeX, BI-TP 93/1
- …