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Blog des Betreibers

Ankündigung: Neuer Stand von Quantum Algebra

Vor geraumer Zeit wurde von mir eine Ergänzung zu Quantum Algebra veröffentlicht. Diese Ergänzung benötigte eine grundlegende Überarbeitung. In der Hauptsache geht es dabei um folgendes:

  1. Behandlung von Notationen in Zusammenhang mit unteren und oberen Indizes. Es geht hier um Verbesserungen, um Mehrdeutigkeiten von Indizes zu vermeiden, z.B. obere Indizes und Potenzausdrücke.
  2. Die Regeln zur Vereinfachung von Operator - Ausdrücken im Sinne der QFT.

Diese grundlegende Überarbeitung wird von mir demnächst veröffentlicht. Dabei wird es auch Notebooks für 3 Anwendungen der Ergänzung geben:

  1. Klein - Gordon - Equation
  2. Dirac - Equation
  3. Maxwell - Equation

 

Details
Kategorie: Blog des Betreibers
Zugriffe: 865

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  • SELECT `c2`.`language`,CONCAT_WS(':', `c2`.`id`, `c2`.`alias`) AS `id`,CONCAT_WS(':', `ca`.`id`, `ca`.`alias`) AS `catid` FROM `jos_content` AS `c` INNER JOIN `jos_associations` AS `a` ON `a`.`id` = `c`.`id` AND `a`.`context` = :context INNER JOIN `jos_associations` AS `a2` ON `a`.`key` = `a2`.`key` INNER JOIN `jos_content` AS `c2` ON `a2`.`id` = `c2`.`id` INNER JOIN `jos_categories` AS `ca` ON `c2`.`catid` = `ca`.`id` AND `ca`.`extension` = :extension2 WHERE `c`.`id` = :id AND c2.access IN (1,5) AND c2.language != 'de-DE' AND (c2.publish_up IS NULL OR c2.publish_up <= '2025-04-05 23:41:50') AND (c2.publish_down IS NULL OR c2.publish_down >= '2025-04-05 23:41:50') AND c2.state = 11.49ms1.47KBParams/libraries/src/Language/Associations.php:145Copy
  • SELECT m.id, m.title, m.module, m.position, m.content, m.showtitle, m.params,am.params AS extra, 0 AS menuid, m.publish_up, m.publish_down FROM jos_modules AS m LEFT JOIN jos_extensions AS e ON e.element = m.module AND e.client_id = m.client_id LEFT JOIN jos_advancedmodules as am ON am.module_id = m.id WHERE m.published = 1 AND e.enabled = 1 AND m.client_id = 0 ORDER BY m.position, m.ordering2.45ms178.17KB/plugins/system/advancedmodules/src/Helper.php:199Copy
  • SELECT m.condition_id,m.item_id FROM jos_conditions_map as m LEFT JOIN jos_conditions as c ON c.id = m.condition_id WHERE `m`.`extension` = 'com_advancedmodules' AND `c`.`published` = 11.05ms1.19KB/administrator/components/com_conditions/src/Model/ItemModel.php:831Copy
  • SHOW FULL COLUMNS FROM `jos_conditions`1.59ms1.45KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:587Copy
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  • SELECT * FROM jos_conditions_rules as r WHERE r.group_id = 8958μs832B/administrator/components/com_conditions/src/Model/GroupModel.php:108Copy
  • SELECT m.extension,m.item_id,m.table,m.name_column FROM jos_conditions_map as m WHERE m.condition_id = 16 ORDER BY m.extension,m.item_id930μs704B/administrator/components/com_conditions/src/Model/ItemModel.php:917Copy
  • SELECT `id`,`title` AS `value` FROM `jos_modules`967μs2.06KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
  • SHOW FULL COLUMNS FROM `jos_modules`1.69ms4.08KB/libraries/vendor/joomla/database/src/Mysqli/MysqliDriver.php:587Copy
  • SELECT `id`,`published` AS `value` FROM `jos_modules`982μs2.06KB/administrator/components/com_conditions/src/Helper/Helper.php:184Copy
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  • SELECT `c2`.`language`,`c2`.`id` FROM `jos_menu` AS `c` INNER JOIN `jos_associations` AS `a` ON `a`.`id` = `c`.`id` AND `a`.`context` = :context INNER JOIN `jos_associations` AS `a2` ON `a`.`key` = `a2`.`key` INNER JOIN `jos_menu` AS `c2` ON `a2`.`id` = `c2`.`id` WHERE `c`.`id` = :id1.03ms1.38KBParams/libraries/src/Language/Associations.php:145Copy
  • SELECT `a`.`id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,CASE WHEN `a`.`publish_up` IS NULL THEN `a`.`created` ELSE `a`.`publish_up` END AS `publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`metadata`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`featured`,`a`.`language`,LENGTH(`a`.`fulltext`) AS `readmore`,`a`.`ordering`,`fp`.`featured_up`,`fp`.`featured_down`,CASE WHEN `c`.`published` = 2 AND `a`.`state` > 0 THEN 2 WHEN `c`.`published` != 1 THEN 0 ELSE `a`.`state` END AS `state`,`c`.`title` AS `category_title`,`c`.`path` AS `category_route`,`c`.`access` AS `category_access`,`c`.`alias` AS `category_alias`,`c`.`language` AS `category_language`,`c`.`published`,`c`.`published` AS `parents_published`,`c`.`lft`,CASE WHEN `a`.`created_by_alias` > ' ' THEN `a`.`created_by_alias` ELSE `ua`.`name` END AS `author`,`ua`.`email` AS `author_email`,`uam`.`name` AS `modified_by_name`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,COALESCE(NULLIF(ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1), 0), 0) AS `rating`,COALESCE(NULLIF(`v`.`rating_count`, 0), 0) AS `rating_count` FROM `jos_content` AS `a` LEFT JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_users` AS `ua` ON `ua`.`id` = `a`.`created_by` LEFT JOIN `jos_users` AS `uam` ON `uam`.`id` = `a`.`modified_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE `a`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`access` IN (:preparedArray3,:preparedArray4) AND `c`.`published` = 1 AND `a`.`state` = :condition AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`language` IN (:preparedArray5,:preparedArray6) ORDER BY a.hits DESC LIMIT 52.88ms63.08KBParams/libraries/src/MVC/Model/BaseDatabaseModel.php:164Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.44ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.54ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.31ms3.98KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.34ms4.02KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `c`.`id`,`c`.`asset_id`,`c`.`access`,`c`.`alias`,`c`.`checked_out`,`c`.`checked_out_time`,`c`.`created_time`,`c`.`created_user_id`,`c`.`description`,`c`.`extension`,`c`.`hits`,`c`.`language`,`c`.`level`,`c`.`lft`,`c`.`metadata`,`c`.`metadesc`,`c`.`metakey`,`c`.`modified_time`,`c`.`note`,`c`.`params`,`c`.`parent_id`,`c`.`path`,`c`.`published`,`c`.`rgt`,`c`.`title`,`c`.`modified_user_id`,`c`.`version`, CASE WHEN CHAR_LENGTH(`c`.`alias`) != 0 THEN CONCAT_WS(':', `c`.`id`, `c`.`alias`) ELSE `c`.`id` END as `slug` FROM `jos_categories` AS `s` INNER JOIN `jos_categories` AS `c` ON (`s`.`lft` < `c`.`lft` AND `c`.`lft` < `s`.`rgt` AND `c`.`language` IN (:preparedArray3,:preparedArray4)) OR (`c`.`lft` <= `s`.`lft` AND `s`.`rgt` <= `c`.`rgt`) WHERE (`c`.`extension` = :extension OR `c`.`extension` = 'system') AND `c`.`access` IN (:preparedArray1,:preparedArray2) AND `c`.`published` = 1 AND `s`.`id` = :id ORDER BY `c`.`lft`1.21ms4KBParams/libraries/src/Categories/Categories.php:375Copy
  • SELECT `alias` FROM `jos_content` WHERE `id` = :id924μs1.31KBParams/components/com_content/src/Service/Router.php:168Copy
  • SELECT `alias` FROM `jos_content` WHERE `id` = :id1.02ms1.31KBParams/components/com_content/src/Service/Router.php:168Copy
  • SELECT `name`,`element` FROM `jos_extensions` WHERE `type` = 'plugin' AND `folder` = 'finder' AND `enabled` = 1986μs656B/administrator/components/com_finder/src/Helper/LanguageHelper.php:135Copy
  • SELECT `title` FROM `jos_finder_taxonomy` WHERE `parent_id` = 1 AND `state` = 1 AND `access` IN (1,5)992μs584B/administrator/components/com_finder/src/Indexer/Taxonomy.php:325Copy
  • SELECT a.params FROM jos_advancedmodules AS a WHERE a.module_id = 106852μs520B/plugins/system/advancedmodules/src/Helper.php:159Copy
  • SELECT a.params FROM jos_advancedmodules AS a WHERE a.module_id = 95857μs520B/plugins/system/advancedmodules/src/Helper.php:159Copy
  • SELECT * FROM `jos_schemaorg` WHERE `itemId` = :itemId AND `context` = :context1.04ms1.55KBParams/plugins/system/schemaorg/src/Extension/Schemaorg.php:403Copy
  • SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `jos_content` AS `a` INNER JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0 AND `a`.`language` IN (:preparedArray1,:preparedArray2)) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray3,:preparedArray4)1.38ms6.23KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
  • SELECT `a`.`id`,`a`.`asset_id`,`a`.`title`,`a`.`alias`,`a`.`introtext`,`a`.`fulltext`,`a`.`state`,`a`.`catid`,`a`.`created`,`a`.`created_by`,`a`.`created_by_alias`,`a`.`modified`,`a`.`modified_by`,`a`.`checked_out`,`a`.`checked_out_time`,`a`.`publish_up`,`a`.`publish_down`,`a`.`images`,`a`.`urls`,`a`.`attribs`,`a`.`version`,`a`.`ordering`,`a`.`metakey`,`a`.`metadesc`,`a`.`access`,`a`.`hits`,`a`.`metadata`,`a`.`featured`,`a`.`language`,`fp`.`featured_up`,`fp`.`featured_down`,`c`.`title` AS `category_title`,`c`.`alias` AS `category_alias`,`c`.`access` AS `category_access`,`c`.`language` AS `category_language`,`fp`.`ordering`,`u`.`name` AS `author`,`parent`.`title` AS `parent_title`,`parent`.`id` AS `parent_id`,`parent`.`path` AS `parent_route`,`parent`.`alias` AS `parent_alias`,`parent`.`language` AS `parent_language`,ROUND(`v`.`rating_sum` / `v`.`rating_count`, 1) AS `rating`,`v`.`rating_count` AS `rating_count` FROM `jos_content` AS `a` INNER JOIN `jos_categories` AS `c` ON `c`.`id` = `a`.`catid` LEFT JOIN `jos_content_frontpage` AS `fp` ON `fp`.`content_id` = `a`.`id` LEFT JOIN `jos_users` AS `u` ON `u`.`id` = `a`.`created_by` LEFT JOIN `jos_categories` AS `parent` ON `parent`.`id` = `c`.`parent_id` LEFT JOIN `jos_content_rating` AS `v` ON `a`.`id` = `v`.`content_id` WHERE ( (`a`.`id` = :pk AND `c`.`published` > 0 AND `a`.`language` IN (:preparedArray1,:preparedArray2)) AND (`a`.`publish_up` IS NULL OR `a`.`publish_up` <= :publishUp)) AND (`a`.`publish_down` IS NULL OR `a`.`publish_down` >= :publishDown) AND `a`.`state` IN (:preparedArray3,:preparedArray4)2.68ms6.23KBParams/components/com_content/src/Model/ArticleModel.php:215Copy
  • SELECT SUM(CASE WHEN `a`.`next_execution` <= :now THEN 1 ELSE 0 END) AS due_count,SUM(CASE WHEN `a`.`locked` IS NULL THEN 0 ELSE 1 END) AS locked_count FROM `jos_scheduler_tasks` AS `a` WHERE `a`.`state` = 13.67ms1.37KBParams/administrator/components/com_scheduler/src/Model/TasksModel.php:465Copy
  • SELECT `session_id` FROM `jos_session` WHERE `session_id` = ?919μs1KBParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:277Copy
  • UPDATE `jos_session` SET `data` = ? , `time` = ? WHERE `session_id` = ?3.62ms592BParams/libraries/vendor/joomla/session/src/Handler/DatabaseHandler.php:301Copy