1. notice
  3. ไธญๆ–‡
  4. 1. feature
  6. ้€ป่พ‘
  7. 2. ้€ป่พ‘
  8. 3. ้›†ๅˆ่ฎบ
  9. 4. ๆ˜ ๅฐ„
  10. 5. ๅบ
  11. 6. ็ป„ๅˆ
  13. ๅพฎ็งฏๅˆ†
  14. 7. ๅฎžๆ•ฐ
  15. 8. ๆ•ฐๅˆ—ๆž้™
  16. 9. โ„^n
  17. 10. Euclidean ็ฉบ้—ด
  18. 11. Minkowski ็ฉบ้—ด
  19. 12. ๅคš้กนๅผ
  20. 13. ่งฃๆž (Euclidean)
  21. 14. ่งฃๆž (Minkowski)
  22. 15. ่งฃๆž struct ็š„ๆ“ไฝœ
  23. 16. ๅธธๅพฎๅˆ†ๆ–น็จ‹
  24. 17. ไฝ“็งฏ
  25. 18. ็งฏๅˆ†
  26. 19. ๆ•ฃๅบฆ
  27. 20. ็ฝ‘ๆž้™
  28. 21. ็ดง่‡ด
  29. 22. ่ฟž้€š
  30. 23. ๆ‹“ๆ‰‘ struct ็š„ๆ“ไฝœ
  31. 24. ๆŒ‡ๆ•ฐๅ‡ฝๆ•ฐ
  32. 25. ่ง’ๅบฆ
  34. ๅ‡ ไฝ•
  35. 26. ๆตๅฝข
  36. 27. ๅบฆ่ง„
  37. 28. ๅบฆ่ง„็š„่”็ปœ
  38. 29. Levi-Civita ๅฏผๆ•ฐ
  39. 30. ๅบฆ่ง„็š„ๆ›ฒ็Ž‡
  40. 31. Einstein ๅบฆ่ง„
  41. 32. ๅธธๆˆช้ขๆ›ฒ็Ž‡
  42. 33. simple-symmetric-space
  43. 34. ไธปไธ›
  44. 35. ็พคไฝœ็”จ
  45. 36. ็ƒๆžๆŠ•ๅฝฑ
  46. 37. Hopf ไธ›
  48. ๅœบ่ฎบ
  49. 38. ้ž็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  50. 39. ็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  51. 40. ็บฏ้‡ๅœบ
  52. 41. ็บฏ้‡ๅœบ็š„ๅฎˆๆ’ๆต
  53. 42. ้ž็›ธๅฏน่ฎบ็บฏ้‡ๅœบ
  54. 43. ๅ…‰้”ฅๅฐ„ๅฝฑ
  55. 44. ๆ—ถ็ฉบๅŠจ้‡็š„่‡ชๆ—‹่กจ็คบ
  56. 45. Lorentz ็พค
  57. 46. ๆ—‹้‡ๅœบ
  58. 47. ๆ—‹้‡ๅœบ็š„ๅฎˆๆ’ๆต
  59. 48. ็”ต็ฃๅœบ
  60. 49. ๅผ ้‡ๅœบ็š„ Laplacian
  61. 50. Einstein ๅบฆ่ง„
  62. 51. ็›ธไบ’ไฝœ็”จ
  63. 52. ่ฐๆŒฏๅญ้‡ๅญๅŒ–
  64. 53. ๆ—‹้‡ๅœบๆ‚้กน
  65. 54. ๅ‚่€ƒ
  67. English
  68. 55. notice
  69. 56. feature
  71. logic-topic
  72. 57. logic
  73. 58. set-theory
  74. 59. map
  75. 60. order
  76. 61. combinatorics
  78. calculus
  79. 62. real-numbers
  80. 63. limit-sequence
  81. 64. โ„^n
  82. 65. Euclidean-space
  83. 66. Minkowski-space
  84. 67. polynomial
  85. 68. analytic-Euclidean
  86. 69. analytic-Minkowski
  87. 70. analytic-struct-operation
  88. 71. ordinary-differential-equation
  89. 72. volume
  90. 73. integral
  91. 74. divergence
  92. 75. limit-net
  93. 76. compact
  94. 77. connected
  95. 78. topology-struct-operation
  96. 79. exponential
  97. 80. angle
  99. geometry
  100. 81. manifold
  101. 82. metric
  102. 83. metric-connection
  103. 84. geodesic-derivative
  104. 85. curvature-of-metric
  105. 86. Einstein-metric
  106. 87. constant-sectional-curvature
  107. 88. simple-symmetric-space
  108. 89. principal-bundle
  109. 90. group-action
  110. 91. stereographic-projection
  111. 92. Hopf-bundle
  113. field-theory
  114. 93. point-particle-non-relativity
  115. 94. point-particle-relativity
  116. 95. scalar-field
  117. 96. scalar-field-current
  118. 97. scalar-field-non-relativity
  119. 98. projective-lightcone
  120. 99. spacetime-momentum-spinor-representation
  121. 100. Lorentz-group
  122. 101. spinor-field
  123. 102. spinor-field-current
  124. 103. electromagnetic-field
  125. 104. Laplacian-of-tensor-field
  126. 105. Einstein-metric
  127. 106. interaction
  128. 107. harmonic-oscillator-quantization
  129. 108. spinor-field-misc
  130. 109. reference

note-math

At first glance, the quotient of Euclidean projective space seems trivial, but once generalized to complex quaternions, the seemingly non-trivial Hopf bundle, a type of fiber bundle, appears. The real case is the bundle. The case of the quaternion Hopf bundle may also be related to the construction of exotic .

or complex number version of Hopf-bundle

[Hopf-bundle]

Embedding , in use as stereographic-projection coordinates

The transformation function of the two coordinates of stereographic projection or

does not change the projective result e.g.

is a bundle on

Construct bundle coordinates with two stereographic projection coordinates

and

And the transformation function or

You can first quotient

At this point, the representation of stereographic projection

does not change the projective result

is a bundle on

Construct bundle coordinates with two stereographic projection coordinates

and

And the transformation function or