Tuesday, 11 March 2025

Clifford Algebra Note 5 TOMONAGA’s Super Multi-time Theory 2008

  

Clifford Algebra

 

Note 5

TOMONAGA’s Super Multi-time Theory

 

TANAKA Akio

 

1 <Schrödinger equation>

State vector     ψ

Time     t

Electromagnetic field     A

Hamiltonian     H

iψ(t) = (t),   ψ(0) = ψ     (1)

2 <Dirac’s paraphrase of Schrödinger equation >

Coordinate     x

Momentum     p

Electron     N in number

Electromagnetic field     A

H-em     Electromagnetic field Hamiltonian

H-em Hn xnpn(xn) ) +   ] ψ(t) = 0     (2)

3 <Representation by unitary transformation>

u(t) = expH-emt }

(xnt) u(t) A (xn) u(t)-1

Φ(t) = u(t) ψ(t)

Hn xnpn(xnt) ) +   ] Φ(t) = 0     (3)

4 < Dirac’s multi-time theory- Time variant in number >

[Hn xnpn(xntn) ) +   ] Φx1, t1; … ; xN, tN ) = 0     (4)

5 <Tomonaga’s representation of electromagnetic field>

Unitary transformation

U (t) = exp {  (H1 + H2 ) t }    

Schrödinger equation

[HH2 + H12  ] ψ(t) = 0    

Independent time variant txyz at each point in space 

H12 (xyztxyz ) +   ] Φ(t) = 0     (5)

6 < Tomonaga’s super multi-time theory>

Super curved surface     C

Point on C     P

4-dimensional volume’s transformation of     CP

Infinite small variation of state vectorΦ[C] = Φ[Txyz]      Φ[C]

H12 P ) +   ] Φ[C] = 0     (6)

 

[References]

<Past work on multi-time themes>

Aurora Theory / Dictoron, Time and Symmetry <Language Multi-Time Conjecture> / Tokyo October 6, 2006

Aurora Theory / Word, Phrase and Sentence <Language Multi-Time Conjecture 2> / Tokyo October 25, 2006

Aurora Theory / Distance and Time <Language Multi-Time Conjecture 3> 5th Time for KARCEVSKIJ / Tokyo October 28, 2006

Language and Spacetime / Time Flow in Word For KOBARI Akihiro and His Time / Tokyo May 3, 2007

<For more details>

Invitation by Theme-Time / Data Arranged at Tokyo January 6, 2008

Aurora Theory

Language and Spacetime

 

Tokyo January 25, 2008

Sekinan Research Field of Language

www.sekinan.com

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