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Jul 2018

For translational

invariant functions

The Lebesgue measure is an example of such a function;

In geometry, a translation "slides"

a thing by a: Ta(p) = p + a.

In physics and mathematics,

continuous translational symmetry

is the invariance of a system of

equations under any translation.

Discrete translational symmetry

is invariant under discrete translation;

Analogously an operator A on functions

is said to be translationally invariant

with respect to a translation operator

{\display style T*{\delta }} T*{\delta }

if the result after applying A doesn't change

if the argument function is translated.

More precisely it must hold that:

{\display style \for all \delta \

Af=A(T*{\delta }f).\,} *

\for all \delta \ Af=A(T{\delta

}f).\,

Laws of physics are translationally invariant

under a spatial translation

if they do not distinguish

different points in space.

According to Noether's theorem,

space translational symmetry of a physical system

is equivalent to the momentum conservation law.

Translational symmetry of any woman

means that a particular translation does not change her.

For a given woman, the translations

for which this applies form a group,

the symmetry group, or, if the women

have more kinds of symmetry, a subgroup of the symmetry group.

invariant functions

The Lebesgue measure is an example of such a function;

In geometry, a translation "slides"

a thing by a: Ta(p) = p + a.

In physics and mathematics,

continuous translational symmetry

is the invariance of a system of

equations under any translation.

Discrete translational symmetry

is invariant under discrete translation;

Analogously an operator A on functions

is said to be translationally invariant

with respect to a translation operator

{\display style T

if the result after applying A doesn't change

if the argument function is translated.

More precisely it must hold that:

{\display style \for all \delta \

Af=A(T

\for all \delta \ Af=A(T

}f).\,

Laws of physics are translationally invariant

under a spatial translation

if they do not distinguish

different points in space.

According to Noether's theorem,

space translational symmetry of a physical system

is equivalent to the momentum conservation law.

Translational symmetry of any woman

means that a particular translation does not change her.

For a given woman, the translations

for which this applies form a group,

the symmetry group, or, if the women

have more kinds of symmetry, a subgroup of the symmetry group.

Wikipedia