# Questions tagged [constrained-dynamics]

A constraint is a condition on the variables of a dynamical problem that the variables (or the physical solution for them) must satisfy. Normally, it amounts to restrictions of such variables to a lower-dimensional hypersurface embedded in the higher-dimensional full space of (unconstrained) variables.

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### Constraints Generating Gauge Transformations and BRST

Given a gauge-invariant point particle action with first class primary constraints $\phi_a$ of the form $$S = \int d \tau[p_I \dot{q}^I - u^a \phi_a]$$ we know immediately, since first class 'primary' ...
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### Primary constraint of electrodynamics

I have some problems understanding the transition from the Lagrangian to Hamiltonian formalism of electrodynamics. I will use the metric $(-+++)$. I want to start from the Lagrangian which is ...
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### Understanding a supersymmetric quantum mechanical gauge theory model

I'm studying this paper on supersymmetric ground state wavefunctions. In section 5 "quantum mechanical gauge theories", it says: "We begin with the ${\cal N} = 2$ gauge theory which ...
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### Why can't we "simply" quantize Maxwell's equations without a Lagrangian to create a quantum theory of electrodynamics?

Useful quantum field theories like quantum electrodynamics (QED) suffer from a litany of problems related to the fact that, at least in their usual Lagrangian formulation, interactions between the ...
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### Dirac procedure for Wheeler De Witt equation

After computing the Hamiltonian constraint and the momentum constraint in general relativity the Hamiltonian constraint is turned into an operator equation and solved in a manner similar to a ...
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### Classical Mechanics proof Lagrangian constraint forces

I've got a simple mathematical question. I was studying the Lagrangian approach of classical mechanics and in this part I had the intention of proving that the differential of the Lagrangian is equal ...
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### Massive vs. massless relativistic point particle in einbein form: Difference in the gauge structure?

The action for the relativistic point particle with mass $m \geq 0$ in a curved background is given by: \begin{equation} S[X] = \int_{\tau_0}^{\tau_1} d\tau \left[ e(\tau)^{-1} g_{\mu \nu}(X(\tau)) \...
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### Why introduce Lagrange multipliers? [duplicate]

For a non-relativistic particle of mass $m$ with a conservative force with potential $U$ acting on the particle and a holonomic constraint given by $f(\mathbf{r},t)=0$, the system can be incorporated ...
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### Simple Lagrangian with free bound and constraint

Let $\alpha,\beta$ non-zero real numbers, $f$ a function of time. I define $L_1=\alpha f + \beta$ and $L_2=p(t) L_1$. I want to minimize $\int_0^T L_2$ under the constraint $\int_0^T L_1=v$, with $T$ ...
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### Why is it ok to set the dilaton to its classical value in Jackiw-Teitelboim (JT) gravity?

I am reading arXiv:1606.01857 (Maldacena-Stanford-Yang), one of the main papers on Jackiw-Teitelboim (JT) gravity. To derive the Schwarzian action, they use the classical solution for the dilaton, eq....
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### Conceptual problem with incorporating constraints to a particular variational principle problem

Consider the following problem: A vector field $\boldsymbol{F}(x)$ is defined over a finite region $V$. A functional of the form \begin{equation} U = \int_V u(\boldsymbol{F})\ d^3x \end{equation} is ...
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