2. Quantum communication link waves

Let , be the space-time constituted by the particles x1ð Þt , x2ð Þt , x3ð Þt , …, whose states φ1, φ2, φ3, … are such that satisfies Eq. (3); then the information is transmitted like the quantum wave ϕ, of the state φ, replaced with the state φ0 i, ið Þ ¼ 1, 2, 3, … , in the infinite homomorphism (which is of the type ϕð Þ¼ n ∗ m ϕð Þ n ϕð Þ m ):

$$
\phi \left( \mathbf{t}\_{\boldsymbol{\uprho}'1} \ast \mathbf{t}\_{\boldsymbol{\uprho}'2} \ast \mathbf{t}\_{\boldsymbol{\uprho}'3} \ast \mathbf{t}\_{\boldsymbol{\uprho}'4} \cdots \right) = \phi\_{\boldsymbol{\uprho}\_1} \left( \mathbf{t}\_{\boldsymbol{\uprho}'1} \right) \phi\_{\boldsymbol{\uprho}\_2} \left( \mathbf{t}\_{\boldsymbol{\uprho}'2} \right) \phi\_{\boldsymbol{\uprho}\_3} \left( \mathbf{t}\_{\boldsymbol{\uprho}'3} \right) \phi\_{\boldsymbol{\uprho}\_4} \left( \mathbf{t}\_{\boldsymbol{\uprho}'4} \right) \cdots \tag{4}
$$

where the transmission of the quantum wave is realised on the spinor space (see spinor technology [6]) of t<sup>σ</sup> and where t<sup>σ</sup> is the intertwining technology that is created in the class σ:

The states of distinguishable particles that are bosons or fermions realise the arrangement that eliminates an infinity of the states that by their sum of spins are annulled, remaining only those that realise an effective action. These are annulled between the perturbed states and those that are affected by scattering. We consider again the space of configuration Cn, <sup>m</sup>, equivalent to the complex given for C Mð Þ, which can be thought as composed for n�hypercubes U, defined by 000…0 boxes. Then we can define a net of paths that will be able to establish routes of organised transformations on diagrams of Feynman type (with path integrals with actions given by Oc and path integrals as Eq. (1)). Likewise the ideal route of the intention is established, considering the action in every node of the net.

Then these arrangements can happen in the nets designed on a field of particles that can be arranged in 0000…0 boxes [7], where the action can be calculated in a point (node of the crystalline net of a field [7]) corresponding to the n� states of energy φið Þ i ¼ 1, 2, 3, …, n , having the superposition n the node given for

$$\oint [\mathbf{x}]\_U = \int\_{000\cdots 0\cdots 0\cdots \text{box}} d\mathbf{z}^n \phi(\mathbf{X}^{a\_1} \mathcal{W}\_{a\_1}) \phi(\mathbf{X}^{a\_2} \mathcal{W}\_{a\_2'}) \cdots \phi(\mathbf{X}^{a\_n} \mathcal{W}\_{a'\_n}) \tag{5}$$

In the quantum zone, the quantum particles field is permanent and interminable, since matter and energy are equivalent and the electrons are interminable and thus the photon production also. What gets worn is that there are the linkages between atoms which can weaken or get lost for the absence of a transmission of the states of suitable energy (routes given by path integrals). Infiltrating the intention on every path γ and under the condition of permanent field given by the operators Oc, the transmission of the states will be revitalised by every node, transmitting the

of photons through a process derived from certain spintronic devices as dots, magnetons, etc., the bosons can be conformed to the information of the communication in waveform and the plasmons as a quantum media of transmission of these information waves. The gauge bosons also will be necessary as transmission nodes. If we want to obtain voice communication, this will be obtained introducing phonons [5] in the photonic wave. We establish some fundamental precisions using quantum mechanics to explain those particles intertwining. We must consider that to that this intertwining happens, are necessary more dimensions that Minkowski

We consider a particle system <sup>p</sup>1, p2, … in a space-time <sup>M</sup> ffi <sup>R</sup>4. Let

a defined force exists given by the action I, of X, along the geodesic γt, and

field gives direction to every field particle φi, having their tangent bundle has a

, ∂μφ<sup>i</sup> � �, which produces one ith-spinor field φ<sup>i</sup>

We can to extend these to whole space Ω Γð Þ⊂ M, on all the elections of possible paths whose statistical weight corresponds to the determined one by the intention of the field, and realising the integration in paths for an infinity of particles-fields in

i

� �<sup>1</sup>=<sup>2</sup> is the amplitude of their propagator. Then we have the

1 B þ ð∞

dφ<sup>1</sup> <sup>B</sup> <sup>⋯</sup> þ ð∞

dφ<sup>n</sup> <sup>B</sup> <sup>⋯</sup>

�∞

ð Þ x sð Þ (1)

: C Mð Þ� Ω ∗ ð Þ! M R, where Ω ∗ ð Þ M is

ω ¼ <I, dω> (2)

�∞

I, of the field X, infiltrates and transmits from particle to particle in whole space Ω Γð Þ, using a configuration given by their Lagrangian L (conscience operator), along

ω φð Þ¼ ð Þ <sup>x</sup> lim <sup>N</sup> ! <sup>∞</sup> <sup>δ</sup>s!<sup>0</sup>

corresponding Feynman integral of the volume form ω φð Þ ð Þ x , obtaining the real path of the particle (where we have chosen quantized trajectories, that is to say,

Then to a configuration on the space-time M, given for C Mð Þ, in a space-time region where there have been interfered paths in the experiment given by multiple split,

dð Þ φð Þ x : But this superposition of paths is realised under an action whose

some dual complex ('forms on configuration spaces'), and then the 'Stokes

ð

Ω�C

, on every particle pi ¼ xið Þt , ið Þ ¼ 1, 2, 3, … : Then a direct intention is the

determines direction by their tangent bundle given for TX<sup>1</sup>

Advances in Quantum Communication and Information

spinor bundle <sup>S</sup>, where the field <sup>X</sup> comes given as <sup>X</sup> <sup>¼</sup> <sup>P</sup>

all the trajectories of Ω Γð Þ: Then of a sum of trajectories, <sup>Ð</sup>

ð

TΩ Γð Þ

þ ð∞

�∞ e iI φ<sup>i</sup> ;∂μφ<sup>i</sup> ½ �dφ

corresponding energy Lagrangian is ω φð Þ¼ ð Þ x I<sup>ξ</sup>ð Þ <sup>x</sup> dð Þ φð Þ x :

<sup>¼</sup> <sup>Y</sup><sup>∞</sup> i¼1

dð Þ φð Þ x , on all the possible field configurations Cn, <sup>m</sup>:

map or connection <sup>∇</sup><sup>I</sup> : <sup>T</sup>Ω Γð Þ! <sup>T</sup><sup>1</sup>

It, a trajectory, which predetermines a position x∈R<sup>3</sup>

t∈It: Also we consider the field X, which infiltrates their action to whole space of points x1ð Þt , x2ð Þt , x3ð Þt , … ∈ Ω Γð Þ, predetermining the points φið Þ xið Þt , that are field particles of the field X and evaluated in the position of every particle. In each point,

, for all time

ð Þ Ω Γð Þ ; that is to say, the

, <sup>φ</sup><sup>i</sup> ð Þ, <sup>∀</sup>φ1, <sup>φ</sup>2,

DFð Þ x tð Þ , one has the

, where the action

i φ<sup>i</sup> <sup>∂</sup> ∂φ<sup>i</sup> � � � xi

ð Þ Ω Γð Þ ,ð Þ ≃T ∗ M , with the rule of correspon-

space-time dimension.

x tð Þ<sup>∈</sup> Ω Γð Þ⊂R<sup>3</sup>

φ3, … ∈ X<sup>1</sup>

sumÐ

Ð

4

dence xi, ∂txi � �↦ φ<sup>i</sup>

TΩ Γð Þ, is had that

where <sup>B</sup> <sup>¼</sup> <sup>m</sup>

theorem' holds

2π iδs

given for <sup>Ω</sup>ð Þ <sup>M</sup> , we have the pairing <sup>Ð</sup>

I φ<sup>i</sup> ð Þ <sup>x</sup> � � <sup>¼</sup> same information about every 0000…0 box, we will call this characteristic an intentionality [8]. However, every particle with regard to others takes their corresponding position, since they all have the same infiltrated intention, by what the synergic action is realised.

References

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DOI: http://dx.doi.org/10.5772/intechopen.89069

Introductory Chapter: Advanced Communication and Nano-Processing of Quantum Signals

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2015;4(3):10-14

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[7] Bulnes F. Teoría de Algoritmos para la Maestría de Informática Aplicada,

[8] Bulnes F. Quantum intentionality and determination of realities in the spacetime through path integrals and their integral transforms. In: Bracken P, editor. Advances in Quantum Mechanics. Rijeka, Croatia: IntechOpen; 2013. DOI: 10.5772/53439. Available from: https:// www.intechopen.com/books/advancesin-quantum-mechanics/quantumintentionality-and-determination-ofrealities-in-the-space-time-through-

Informáticas (UCI); Habana, Cuba; Postdoctoral Project (Aplicaciones de la Teoría Infinita de Lie y sus Aplicaciones

Universidad de las Ciencias

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path-integrals-and-t

7

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