discrete symmetries造句

• A discrete symmetry group is a symmetry group that is a discrete isometry group.
• As such, it does not apply to discrete symmetries or globally for Lie groups.
• Discrete symmetries are described by discrete groups.
• In it are discussed discrete symmetries.
• That the theorem does not apply to discrete symmetries can be seen in the two-dimensional Ising model.
• Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups ( see Symmetry group ).
• A "'discrete symmetry "'is a symmetry that describes non-continuous changes in a system.
• Further, the large-scale topology of the universe should impose restrictions on the solutions, such as quantization or discrete symmetries.
• The third discrete symmetry entering in the CPT theorem along with and, charge conjugation symmetry, has nothing directly to do with Lorentz invariance.
• Discrete symmetries sometimes involve some type of'swapping', these swaps usually being called " reflections " or " interchanges ".
• The phase transition between a liquid and a crystal is a transition that reduces the continuous translation symmetry of the liquid to the discrete symmetry of the crystal.
• The vacuums are separated by the surface of the NTS representing a domain wall configuration ( topological defect ), which also appears in field theories with broken discrete symmetry.
• However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a vacuum state of the full quantum theory, although a classical solution may break a continuous symmetry.
• They provide a natural framework for analysing the continuous symmetries of differential equations ( differential Galois theory ), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations.
• A "'discrete symmetry group "'is a symmetry group such that for every point of the space the set of images of the point under the isometries in the symmetry group is a discrete set.
• They provide a natural framework for analysing the continuous symmetries of differential equations ( Differential Galois theory ), much in the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations.
• From this explanation one can see why the Ising model magnet with discrete symmetry has no spin waves : the notion of spreading a disturbance in the spin lattice over a long wavelength makes no sense when spins have only two possible orientations.
• It has now been shown that this is not necessarily true : When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant ( in the renormalization group sense ) anisotropies, then some exponents ( such as \ gamma, the exponent of the susceptibility ) are not identical.
• Discrete symmetry groups come in three types : ( 1 ) finite "'point groups "', which include only rotations, reflections, inversion and rotoinversion  they are just the finite subgroups of O ( " n " ), ( 2 ) infinite "'categorization of subgroups of the Euclidean group corresponds a categorization of symmetry groups.
• Note that the Ising model exhibits the following discrete symmetry : If every spin in the model is flipped, such that { S _ i } \ rightarrow {-S _ i }, where S _ i is the value of the i ^ { th } spin, the Hamiltonian ( and consequently the free energy ) remains unchanged for zero external field ( H = 0 ).