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Therefore, within the range of small wave vectors (continuum approximation)

dispersion law (7) fulfils the relationship

ω

2

l

=

ω

2

0

c

2

k

2

.

(6)

Group velocity of the waves corresponding to the dispersion law (8) can

be written as follows:

dk

=

c

2

k

ω

=

c

2

k

p

ω

2

0

c

2

k

2

.

(7)

According to the relationship (9), in this case phase and group velocities

have mutually opposite directions. Effective mass

m

and rest mass

m

0

of

the longitudinal photons according to expressions (8) and (9) are negative:

m

=

~

d

2

ω

dk

2

=

~

(

ω

2

0

c

2

k

2

)

3

2

c

2

ω

2

;

m

0

=

m

(0) =

~

ω

0

c

2

.

Along with translational degrees of freedom, clusters of the low-temperature

phase of vacuum have respiratory and axion degrees of freedom. Therefore,

two additional dispersion branches corresponding to paraphotons and

axions exist in vacuum besides the branches of the vector photons (see

Fig. 6). The dispersion laws for paraphotons and axions have relativistic

form:

ω

2

=

ω

2

par

+

c

2

0

k

2

;

ω

2

=

ω

2

ax

+

c

2

0

k

2

.

Photon-boson conversion. Generation of paraphotons, axions,

and longitudinal photons in the laboratory.

Quantum description of

the photon-boson conversion processes in the material media and in

physical vacuum is performed on the basis of introduction of Hamiltonian

anaharmonical terms

H

=

H

01

+

H

02

+

V

;

V

=

f

1

[

a

(

a

0

)

+

b

+

+

a b

(

a

0

)

+

] +

f

2

[

a

(

a

0

)

b

+

+

b a

+

(

a

0

)

+

]

.

Here

Н

01

and

Н

02

are Hamiltonian functions of photon and boson fields in

harmonic approximation;

V

is an excitation operator;

a

,

a

0

,

b

,

b

,

a

+

,

(

a

0

)

+

,

b

,

b

+

are operators of annihilation and genesis of photon and boson fields.

Probability of the respective processes of photon-boson conversion is

given by the expressions

W

fi

=

2

π

~

f

2

1

[

n

0

(

n

0

+ 1)(

m

b

+ 1) +

n

0

m

b

(

n

0

+ 1)] ;

W

fi

=

2

π

~

f

2

2

[

n

2

0

(

m

b

+ 1) +

m

b

(

n

0

+ 1)(

n

0

+ 1)]

.

ISSN 1812-3368. Herald of the BMSTU. Series “Natural Sciences”. 2015. No. 1

43