lagrangian density sentence in Hindi
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- The Euler Lagrange equations for this Lagrangian density L _ 0 are, with \ xi ( x, y, t ) representing either \ varphi or \ zeta:
- This will certainly be true if the Lagrangian density \ mathcal { L } is left invariant, but it will also be true if the Lagrangian changes by a divergence,
- The three constants of the theory, G, \ mu and \ omega, are promoted to scalar fields by introducing associated kinetic and potential terms in the Lagrangian density:
- The Lagrangian density is the wedge product of that of ordinary Chern Simons theory with the holomorphic ( 3, 0 )-form, which exists in the Calabi-Yau case.
- Let us refer to such a regularization as " the minimal realistic regularization ", and start searching for the corresponding, modified free-field parts of the QED Lagrangian density.
- The evolution operator is obtained in the interaction picture where time evolution is given by the interaction Hamiltonian, which is the integral over space of the second term in the Lagrangian density given above:
- This model allows for topological finite action solutions, as at infinite space-time the Lagrangian density must vanish, meaning " n & # 770; " = constant at infinity.
- Since linear combinations of these quantities are also Lorentz invariant, this leads naturally to the Lagrangian density for the Dirac field by the requirement that the Euler Lagrange equation of the system recover the Dirac equation.
- Characteristic of field theories, the dynamics of the field strength are summarized by a suitable Lagrangian density and substitution into the Euler Lagrange equation ( for fields ) obtains the equation of motion for the field.
- Let \ mathcal { L } _ \ mathrm { M } represent the Lagrangian density of matter and \ mathcal { L } _ \ mathrm { G } represent the Lagrangian density of the gravitational field.
- Let \ mathcal { L } _ \ mathrm { M } represent the Lagrangian density of matter and \ mathcal { L } _ \ mathrm { G } represent the Lagrangian density of the gravitational field.
- To use the Dyson series to calculate anything, one needs more than a gauge-invariant Lagrangian density; one also needs the quantization and gauge fixing prescriptions that enter into the Feynman rules of the theory.
- For example, in the case of Newtonian gravity, the Lagrangian density integrated over spacetime gives you an equation which, if solved, would yield \ Phi ( \ mathbf { x }, t ).
- Dirac s two preceding remarks suggest that we should start searching for a realistic regularization in the case of quantum electrodynamics ( QED ) in the four-dimensional Minkowski spacetime, starting with the original QED Lagrangian density.
- Instead of " fixing " the gauge to a particular " constraint surface " in configuration space, one can break the gauge freedom with an additional, non-gauge-invariant term added to the Lagrangian density.
- The fundamental Lagrangian density of one's theory is presumed to lie in the subspace " Pl " 0 of polynomials which are real-valued and invariant under any unbroken non-gauge symmetry groups.
- Noether's theorem begins with the assumption that a specific transformation of the coordinates and field variables does not change the action, which is defined as the integral of the Lagrangian density over the given region of spacetime.
- In Lagrangian field theory, the Lagrangian as a function of generalized coordinates is replaced by a Lagrangian density, a function of the fields in the system and their derivatives, and possibly the space and time coordinates themselves.
- Using a Taylor series expansion for the second integral around the mean free-surface elevation z = 0, and only retaining quadratic terms in \ Phi and \ zeta, the Lagrangian density L _ 0 for linear wave motion becomes
- To obtain the field equations the electromagnetic tensor in the Lagrangian density needs to be replaced by its definition in terms of the 4-potential " A ", and its this potential which enter the Euler-Lagrange equations.
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